toDenselyNormedField π | CompOp | 2402 mathmath: Matrix.l2_opNorm_toEuclideanCLM, OrthonormalBasis.singleton_repr, Pi.comul_eq_adjoint, instSeparatingDual, Convex.norm_image_sub_le_of_norm_derivWithin_le, TensorProduct.mapInclIsometry_apply, LinearMap.IsSymmetric.clm_adjoint_eq, ContinuousLinearMap.rayleigh_smul, DirectSum.IsInternal.isometryL2OfOrthogonalFamily_symm_apply, InnerProductSpace.Core.inner_smul_right, conj_re, TemperedDistribution.lineDerivOpCLM_eq, Submodule.starProjection_apply_eq_isComplProjection, WithLp.prod_inner_apply, sqrt_eq_ite, ContinuousLinearMap.inner_map_map_of_mem_unitary, integrableOn_cfcβ', ContinuousAt.inner, LinearMap.IsStarProjection.ext_iff, Orthonormal.linearIndependent, im_le_neg_norm_iff_eq_neg_I_mul_norm, SchwartzMap.lineDerivOpCLM_eq, MeasureTheory.lpNorm_conj, AddChar.card_addChar_le, TensorProduct.enorm_lid, InnerProductSpace.Core.inner_add_left, continuous_cfcβHomSuperset_left, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, cfcβL_integral, Matrix.frobenius_nnnorm_mul, pos_iff_exists_ofReal, TensorProduct.inner_tmul, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, one_re, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, MeasureTheory.condExpL1_smul, Submodule.IsCompl.projection_isSymmetricProjection_iff, Orthonormal.inner_left_finsupp, norm_cfcβHom, map_apply, OrthonormalBasis.orthogonalProjection_eq_sum, LinearMap.IsSymmetric.inner_map_polarization, geometric_hahn_banach_point_open, ContinuousLinearMap.integral_compLp, tendsto_birkhoffAverage_apply_sub_birkhoffAverage', LinearMap.adjoint_adjoint, Affine.Simplex.orthogonalProjectionSpan_map, TensorProduct.ext_iff_inner_left, EuclideanGeometry.vsub_orthogonalProjection_mem_direction_orthogonal, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, ofRealCLM_apply, normSq_to_real, IsometricContinuousFunctionalCalculus.isGreatest_nnnorm_spectrum, IsSelfAdjoint.commute_cfcHom, InnerProductSpace.span_gramSchmidtNormed, LinearMap.toLinearMap_tracePositiveLinearMap, cfcβ_norm_nonneg, ContinuousWithinAt.cfcβ, EuclideanGeometry.reflection_orthogonal_vadd, hasFDerivAt_iff_hasGradientAt, reCLM_apply, cfcβHom_apply_mem_elemental, ClosedSubmodule.sub_mem_orthogonal_of_inner_right, IsHilbertSum.surjective_isometry, curveIntegral_smul, div_re_ofReal, ContinuousLinearMap.isSelfAdjoint_iff_isSymmetric, Submodule.reflection_trans_reflection, inner_vsub_right_eq_zero_symm, separate_convex_open_set, Submodule.orthogonalDecomposition_symm_apply, MeasureTheory.taylor_charFun_two, OrthogonalFamily.linearIsometry_apply_single, Filter.Tendsto.cfc, ContinuousLinearMap.isStarProjection_iff_isSymmetricProjection, InnerProductSpace.rankOne_one_left_eq_innerSL, Submodule.IsOrtho.starProjection_comp_starProjection, IsHilbertSum.mkInternal, cfc_mem_elemental, ContDiffAt.implicitFunction_def, LinearMap.IsSymmetric.restrictScalars, StrongDual.norm_extendRCLike, ContinuousLinearMap.opNorm_bound_of_ball_bound, ClosedSubmodule.toSubmodule_orthogonal_eq, Convex.convex_isRCLikeNormedField, LinearMap.instIsOrderedAddMonoidId, nnnorm_cfc_lt, EuclideanSpace.orthonormal_single, Matrix.IsHermitian.det_abs, MeasureTheory.contDiffOn_convolution_left_with_param, ofRealLI_apply, LinearMap.IsPositive.ne_zero_iff, hasDerivAt_integral_of_dominated_loc_of_lip, ContinuousLinearMapWOT.le_nhds_iff_forall_inner_apply_le_nhds, curveIntegrable_segment, LinearMap.isPositive_adjoint_comp_self, Submodule.toLinearEquiv_orthogonalDecomposition_symm, OrthonormalBasis.repr_injective, LinearMap.IsSymmetric.isFinitelySemisimple, re_add_im, InnerProductSpace.Core.inner_mul_inner_self_le, ContinuousLinearMap.IsPositive.inner_left_eq_inner_right, Affine.Simplex.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Matrix.spectrum_toEuclideanLin, hasStrictFDerivAt_of_hasFDerivAt_of_continuousAt, MeasureTheory.norm_condExpL2_le, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, Matrix.IsHermitian.cfc_eq, lp.inner_eq_tsum, ContinuousLinearMap.continuous_integral_comp_L1, ContinuousLinearMapWOT.tendsto_iff_forall_inner_apply_tendsto, ContDiff.hasStrictFDerivAt, star_def, OrthonormalBasis.sum_inner_mul_inner, Matrix.l2_opNorm_mulVec, Submodule.re_inner_starProjection_eq_normSq, conjCLE_norm, ordinaryHypergeometric_radius_top_of_neg_natβ, inner_self_eq_one_of_norm_eq_one, MeasureTheory.inner_condExpL2_left_eq_right, integrableOn_cfc', ContinuousLinearMap.integral_apply, algebraMap_eq_ofReal, Submodule.reflection_orthogonal_apply, SchwartzMap.integral_clm_comp_lineDerivOp_right_eq_neg_left, inner_apply', MeasureTheory.MemLp.const_inner, MeasureTheory.integral_fintype_prod_volume_eq_pow, LinearMap.orthogonal_ker, LinearMap.IsSymmetric.diagonalization_apply_self_apply, EuclideanGeometry.orthogonalProjection_congr, LinearMap.IsPositive.re_inner_nonneg_right, MeasureTheory.iteratedDeriv_charFun_zero, flip_innerSL_real, Matrix.le_iff, norm_cfc_lt_iff, Orientation.volumeForm_robust_neg, Submodule.starProjection_orthogonal', linearIndependent_of_ne_zero_of_wInner_one_eq_zero, norm_I_of_ne_zero, LinearMap.IsSymmetric.im_inner_self_apply, ContinuousLinearMap.IsPositive.toLinearMap, Submodule.toLinearEquiv_orthogonalDecomposition, sub_conj, OrthonormalBasis.toBasis_tensorProduct, re_sqrt_ofReal, TensorProduct.congrIsometry_refl_refl, norm_smul_inv_norm', Module.Dual.extendRCLikeβ_symm_apply, MeasureTheory.condExpL2_ae_eq_zero_of_ae_eq_zero, pos_iff, MeasureTheory.isTightMeasureSet_iff_inner_tendsto, isClosedEmbedding_cfcβAux, AddChar.wInner_cWeight_self, TensorProduct.enorm_comm, innerSL_apply_apply, Submodule.isOrtho_sup_right, HasGradientAt.continuousOn, CFC.abs_eq_cfcβ_coe_norm, Orthonormal.codRestrict, LinearIsometry.rTensor_def, LinearMap.adjoint_innerββ_apply, inner_sum, EuclideanSpace.inner_single_left, EuclideanSpace.basisFun_toBasis, LinearMap.singularValues_zero, Submodule.orthogonalProjectionFn_inner_eq_zero, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, inner_eq_norm_mul_iff, geometric_hahn_banach_of_nonempty_interior_point, map_same_eq_id, LinearMap.adjoint_eq_toCLM_adjoint, ClosedSubmodule.orthogonal_gc, LinearMap.isPositive_id, nnnorm_cfcβ_lt_iff, Matrix.toLinearMap_tracePositiveLinearMap, Submodule.orthogonalProjection_mem_subspace_eq_self, EuclideanSpace.norm_sq_eq, ContinuousLinearMap.IsPositive.inner_nonneg_right, wInner_sub_right, GaussianFourier.integral_cexp_neg_mul_sq_norm_add_of_euclideanSpace, InnerProductSpace.span_gramSchmidtNormed_range, Submodule.orthogonal_disjoint, StrongDual.norm_extendRCLike_bound, LinearMap.isSelfAdjoint_toContinuousLinearMap_iff, Submodule.starProjection_add_starProjection_orthogonal, Matrix.spectrum_toLpLin, ContinuousOn.cfcβ', OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, Submodule.mem_orthogonal_singleton_iff_inner_right, InnerProductSpace.Core.inner_smul_left, ProbabilityTheory.measurePreserving_restrictβ_multivariateGaussian, ContinuousMap.setOfIdeal_ofSet_eq_interior, InnerProductSpace.toDual_symm_apply, OrthogonalFamily.of_pairwise, MeasureTheory.integral_fintype_prod_eq_prod, IsHilbertSum.linearIsometryEquiv_symm_apply, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_same_orientation, Submodule.starProjection_singleton, conj_nat_cast, EuclideanSpace.basisFun_apply, EuclideanGeometry.reflection_symm, RKHS.coe_smul, IsGreatest.nnnorm_cfcβ, ContinuousAt.cfc, Submodule.isOrtho_iff_inner_eq, EuclideanGeometry.orthogonalProjection_contLinear, curveIntegralFun_smul, ClosedSubmodule.mem_orthogonal', ofReal_re, ContinuousLinearMap.ker_le_ker_iff_range_le_range, MeasureTheory.charFun_toDual_symm_eq_charFunDual, EuclideanGeometry.dist_orthogonalProjection_eq_iff_oangle_eq, OrthogonalFamily.orthonormal_sigma_orthonormal, re_add_im_ax, PreInnerProductSpace.Core.smul_left, Differentiable.fderiv_norm_rpow, normSq_neg, curveIntegrable_fun_neg_iff, ContDiffAt.hasStrictDerivAt, toStarOrderedRing, Submodule.reflection_symm, MeasureTheory.integral_const_mul, OrthonormalBasis.det_eq_neg_det_of_opposite_orientation, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces, TensorProduct.ext_iff_inner_right_threefold', CurveIntegrable.zero, is_real_TFAE, OrthonormalBasis.det_to_matrix_orthonormalBasis_of_opposite_orientation, curveIntegrable_smul_iff, TensorProduct.toLinearEquiv_lidIsometry, OrthonormalBasis.toBasis_singleton, ContDiffOn.inner, inner_gradientWithin_right, EuclideanGeometry.reflection_map, ContinuousLinearMap.adjoint_id, InnerProductSpace.smul_left, ClosedSubmodule.inf_orthogonal, ContinuousLinearMap.isPositive_natCast, tendsto_birkhoffAverage_apply_sub_birkhoffAverage, abs_im_div_norm_le_one, norm_sub_mul_self, Submodule.sub_mem_orthogonal_of_inner_left, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, Submodule.starProjection_comp_starProjection_eq_zero_iff, SchwartzMap.laplacianCLM_eq, LinearIsometryEquiv.conjStarAlgEquiv_apply, LinearMap.toMatrixOrthonormal_reindex, MeasureTheory.integral_div, LinearMap.ker_self_comp_adjoint, Matrix.IsHermitian.eigenvalues_eq, Filter.tendsto_ofReal_iff', inner_smul_left_eq_star_smul, norm_cfc_le_iff, mul_conj, norm_conj, borelSpace, im_inner_eq_norm_sub_i_smul_mul_self_sub_norm_add_i_smul_mul_self_div_four, entry_norm_bound_of_unitary, LinearMap.IsSymmetricProjection.ext_iff, ConvexOn.univ_sSup_of_countable_affine_eq, Matrix.PosDef.eigenvalues_pos, hasSum_ofReal, InnerProductSpace.inner_left_rankOne_apply, NonUnitalIsometricContinuousFunctionalCalculus.norm_quasispectrum_le, continuous_normSq, ClosedSubmodule.orthogonal_injective, InnerProductSpace.gramSchmidtNormed_linearIndependent, SchwartzMap.fderivCLM_apply, Module.Dual.re_extendRCLike_apply, difference_quotients_converge_uniformly, Submodule.norm_starProjection_apply_le, ContinuousLinearMap.norm_extendToπ, cfcHom_mem_elemental, cfcβHom_mem_elemental, HasFDerivAt.norm_sq, LinearIsometry.map_starProjection', ofNat_re, polynomialFunctions.starClosure_topologicalClosure, innerββ_apply_apply, OrthonormalBasis.repr_self, ofReal_balance, Submodule.symmetric_isOrtho, OrthogonalFamily.norm_sq_diff_sum, norm_smul_inv_norm, ContinuousLinearMap.eq_adjoint_iff, MeasureTheory.L2.inner_def, Submodule.starProjection_tendsto_self, nonpos_iff, smul_re, nonpos_iff_exists_ofReal, wInner_of_isEmpty, LinearMap.IsSymmetric.directSum_decompose_apply, LinearMap.IsSymmetric.splits_charpoly, Continuous.cfc', realRingEquiv_symm_apply, EuclideanGeometry.reflection_vadd_smul_vsub_orthogonalProjection, ContinuousLinearMap.IsPositive.smul_of_nonneg, InnerProductSpace.rankOne_apply, EuclideanSpace.nndist_eq, Unitary.coe_linearIsometryEquiv_apply, OrthonormalBasis.toBasis_adjustToOrientation, Matrix.IsHermitian.rank_eq_rank_diagonal, Submodule.reflection_singleton_apply, nonUnitalContinuousFunctionalCalculus, HasDerivAt.hasGradientAt, SchwartzMap.compCLMOfContinuousLinearEquiv_apply, intervalIntegral.integral_div, EuclideanGeometry.inter_eq_singleton_orthogonalProjection, isClosed_setOf_tendsto_birkhoffAverage, AnalyticOn.hasFPowerSeriesOnSubball, cfcβ_integral, IsSelfAdjoint.adjoint_eq, Submodule.finrank_add_finrank_orthogonal', LinearMap.isHermitian_toMatrix_iff, OrthonormalBasis.measurePreserving_repr, Submodule.reflection_apply, ofReal_comp_balance, abs_re_le_norm, curveIntegralFun_segment, RKHS.kernel_apply, reCLM_norm, geometric_hahn_banach_closed_point, MeasureTheory.AEStronglyMeasurable.inner_const, Submodule.orthogonal_eq_bot_iff, TensorProduct.adjoint_map, curveIntegral_neg, AEMeasurable.im, cfcβ_setIntegral, HasGradientAt.continuousAt, LinearIsometryEquiv.lTensor_apply, InnerProductSpace.gramSchmidt_def, LinearMap.ker_adjoint_comp_self, ContinuousLinearMap.isPositive_self_comp_adjoint, ofReal_sub, LinearMap.adjoint_toContinuousLinearMap, Affine.Simplex.orthogonalProjectionSpan_eq_point, Unitary.linearIsometryEquiv_coe_apply, Matrix.IsHermitian.eigenvectorUnitary_col_eq, LDL.lowerInv_eq_gramSchmidtBasis, Submodule.starProjection_inner_eq_zero, norm_sq_eq_def_ax, MeasureTheory.MemLp.condExpL2_ae_eq_condExp, ContinuousLinearMap.toSesqForm_apply_coe, SchwartzMap.fourierMultiplierCLM_compL_fourierMultiplierCLM, LinearPMap.adjointAux_unique, LinearIsometryEquiv.adjoint_eq_symm, TensorProduct.mapIsometry_id_id, ordinaryHypergeometricSeries_radius_eq_one, MeasureTheory.setIntegral_prod_mul, Matrix.toEuclideanLin_apply, inner_self_eq_norm_sq_to_K, IsContDiffImplicitAt.hasFDerivAt, Submodule.IsOrtho.orthogonalProjection_comp_subtypeL, LinearMap.IsPositive.isPositive_smul_iff, intCast_re, LinearIsometryEquiv.trans_smul, MeasureTheory.charFunDual_eq_charFun_map_one, EuclideanGeometry.orthogonalProjection_map, im_eq_zero_iff_isSelfAdjoint, IsHilbertSum.hasSum_linearIsometryEquiv_symm, Submodule.IsOrtho.map_iff, MeasureTheory.integral_fintype_prod_eq_pow, norm_ofReal, inner_mul_inner_self_le, Module.Dual.im_extendRCLike_apply, Orthonormal.basisTensorProduct, InnerProductSpace.Core.inner_smul_ofReal_right, LinearEquiv.coe_isometryOfOrthonormal, Matrix.IsHermitian.eigenvalues_eq_eigenvalues_iff, conjCLE_apply, EuclideanSpace.norm_single, mul_im_ax, ProbabilityTheory.IndepFun.integral_comp_mul_comp, Orthonormal.inner_left_fintype, LinearMap.IsSymmetricProjection.sub_of_range_le_range, LinearMap.IsSymmetric.conj_adjoint, InnerProductSpace.Core.norm_eq_sqrt_re_inner, wInner_cWeight_eq_expect, Submodule.coe_orthogonalDecomposition_symm, MeasureTheory.aestronglyMeasurable_condExpL2, I_mul_I, cfcL_integrable, Submodule.orthogonalProjection_bot, ContinuousLinearMap.adjointAux_norm, toIsStrictOrderedModule, coe_basisOfOrthonormalOfCardEqFinrank, abs_re_div_norm_le_one, Submodule.range_starProjection, norm_sub_sq, toIsStrictOrderedRing, LinearIsometryEquiv.inner_map_eq_flip, EuclideanGeometry.angle_orthogonalProjection_self, binomialSeries_radius_eq_one, EuclideanGeometry.orthogonalProjection_apply_mem, intervalIntegral.hasFDerivAt_integral_of_dominated_loc_of_lip, Pi.counit_eq_adjoint, ProbabilityTheory.covarianceBilin_apply_basisFun_self, IsSelfAdjoint.isSymmetric, LinearMap.toMatrixOrthonormal_apply_apply, I_re_ax, MeasureTheory.charFun_apply_real, instCStarRing, LinearPMap.graph_adjoint_toLinearPMap_eq_adjoint, EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eq, Submodule.finrank_add_inf_finrank_orthogonal, Submodule.exists_add_mem_mem_orthogonal, LDL.lowerInv_orthogonal, GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace, HasGradientWithinAt.continuousWithinAt, re_nonneg_of_nonneg, InnerProductSpace.Core.inner_neg_left, ContinuousLinearMap.integral_comp_comm', LinearMap.IsSymmetric.coe_re_inner_self_apply, ContinuousOn.cfc, summable_mul_of_bigO_atTop, AddChar.wInner_cWeight_eq_zero_iff_ne, entrywise_sup_norm_bound_of_unitary, iInter_countable_halfSpaces_eq, hasStrictDerivAt_exp_smul_const, ofReal_nonneg, ContinuousMap.setOfIdeal_ofSet_of_isOpen, EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eq, SchwartzMap.smulLeftCLM_compCLMOfContinuousLinearEquiv, Module.Basis.mulOpposite_is_orthonormal_iff, EuclideanSpace.instFactEqNatFinrankFin, differentiable_euclidean, inrNonUnitalStarAlgHom_comp_cfcβHom_eq_cfcβAux, Finsupp.sum_inner, MeasureTheory.integral_fin_nat_prod_volume_eq_prod, MeasureTheory.condExpL2_indicator_ae_eq_smul, complexRingEquiv_apply, ClosedSubmodule.orthogonal_closure'', contDiffWithinAt_euclidean, hasStrictDerivAt_exp_smul_const', Real.fourier_iteratedFDeriv, re_inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, nonUnitalContinuousFunctionalCalculusIsClosedEmbedding, SchwartzMap.smulLeftCLM_real_smul, InnerProductSpace.toDualMap_apply_apply, Submodule.le_orthogonal_orthogonal, LinearMap.eq_adjoint_iff_basis_left, LinearMap.IsSymmetricProjection.isIdempotentElem, Matrix.PosSemidef.posDef_iff_isUnit, EuclideanSpace.volume_closedBall_fin_three, re_inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two, LinearMap.extendToπ'_apply, curveIntegral_fun_smul, NumberField.mixedEmbedding.euclidean.stdOrthonormalBasis_map_eq, HasFDerivAt.curveIntegral_segment_source, Matrix.IsHermitian.eigenvectorUnitary_mulVec, Submodule.instHasOrthogonalProjectionOfCompleteSpace, InnerProductSpace.unique_continuousLinearMapOfBilin, MeasureTheory.MemLp.inner_const, OrthogonalFamily.linearIsometry_apply_dfinsupp_sum_single, Submodule.orthogonal_orthogonal_monotone, Module.Dual.norm_extendRCLike_apply_sq, curveIntegral_fun_zero, LinearMap.nonneg_iff_isPositive, coe_innerSL_apply, inner_eq_zero_of_right, LinearMap.IsSymmetric.inner_map_self_eq_zero, OrthonormalBasis.prod_apply, inner_re_zero_right, Matrix.PosSemidef.det_sqrt, MeasureTheory.integral_condExpL2_eq, LinearPMap.adjoint_apply_eq, integral_smul_const, range_cfcβHom, toPosMulReflectLT, TensorProduct.lidIsometry_apply, OrthogonalFamily.isInternal_iff_of_isComplete, MeasureTheory.StronglyMeasurable.inner, Convex.exists_forall_hasFDerivAt_of_fderiv_symmetric, Orientation.volumeForm_def, EuclideanSpace.dist_single_same, Module.Basis.coe_toOrthonormalBasis_repr, LinearMap.IsPositive.inner_nonneg_left, norm_cfcβ_lt, hasGradientAtFilter_iff_isLittleO, MeasureTheory.convolution_precompR_apply, ContinuousLinearMap.instCStarRingId, NormedSpace.eq_zero_iff_forall_dual_eq_zero, SchwartzMap.compSubConstCLM_apply, hasGradientAt_iff_isLittleO, MeasureTheory.setIntegral_condExpL2_indicator, InnerProductSpace.nnnorm_rankOne, PreInnerProductSpace.Core.conj_inner_symm, range_cfc_subset, stereographic_apply_neg, OrthonormalBasis.orthogonalProjection_apply_eq_sum, LinearMap.isSymmetric_self_comp_adjoint, Matrix.PosSemidef.trace_eq_zero_iff, InnerProductSpace.Core.norm_inner_symm, HasGradientWithinAt.differentiableWithinAt, ContinuousLinearMap.setIntegral_compLp, LinearMap.trace_eq_sum_inner, Matrix.gram_zero, Submodule.norm_eq_iInf_iff_inner_eq_zero, Module.Dual.extendRCLike_apply, HasCompactSupport.hasDerivAt_convolution_right, InnerProductSpace.isSymmetricProjection_rankOne_self, RKHS.isHermitian_kernel, ProbabilityTheory.complexMGF_mul_I, Matrix.IsHermitian.charpoly_cfc_eq, norm_ofNat, IsGreatest.norm_cfcβ, hasGradientWithinAt_iff_hasFDerivWithinAt, norm_inner_eq_norm_iff, re_monotone, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, DirectSum.IsInternal.subordinateOrthonormalBasis_subordinate, Matrix.gram_eq_conjTranspose_mul, im_ofReal_pow, LinearIsometryEquiv.smul_apply, inner_eq_norm_mul_iff_div, Submodule.topologicalClosure_eq_self, LinearMap.IsSymmetric.card_filter_eigenvalues_eq, FiniteDimensional.RCLike.properSpace_submodule, EuclideanGeometry.dist_orthogonalProjection_eq_of_two_zsmul_oangle_eq, range_stereographic_symm, cfcβ_comp_norm, FiniteDimensional.rclike_to_real, ContinuousLinearMap.norm_eq_iSup_rayleighQuotient, MeasureTheory.contDiffOn_convolution_right_with_param, WeakDual.CharacterSpace.continuousMapEval_bijective, LDL.lowerInv_triangular, Orientation.volumeForm_robust, PiLp.volume_preserving_toLp, LowerSemicontinuousOn.isClosed_re_epigraph, EuclideanGeometry.orthogonalProjection_apply', Affine.Simplex.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, isOpenEmbedding_stereographic_symm, LinearMap.IsSymmetric.hasEigenvalue_iSup_of_finiteDimensional, Polynomial.ofReal_eval, wInner_neg_right, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le, Continuous.cfcβ_of_mem_nhdsSet, inner_self_im, MeasureTheory.contDiffOn_convolution_left_with_param_comp, ofReal_natCast, cfcβHom_integral, EuclideanGeometry.orthogonalProjection_orthogonalProjection_of_le, unitary.linearIsometryEquiv_coe_symm_apply, ContinuousLinearMap.isPositive_def, Continuous.cfcβ, continuousOn_cfc_setProd, RKHS.posSemidef_tfae, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, SchwartzMap.toBoundedContinuousFunctionCLM_apply, conj_ofReal, curveIntegral_segment, OrthonormalBasis.coe_ofRepr, Submodule.starProjection_top', EuclideanGeometry.Sphere.isTangent_iff_isTangentAt_orthogonalProjection, OrthonormalBasis.toBasis_mulOpposite, Submodule.adjoint_subtypeL, IsGreatest.norm_cfc, hasStrictFDerivAt_exp, inner_re_zero_left, IsCoercive.range_eq_top, gauge_norm_smul, EuclideanSpace.nnnorm_single, LinearMap.isSymmetric_adjoint_mul_self, InnerProductSpace.Core.cauchy_schwarz_aux, inner_self_ofReal_re, conjLIE_apply, Submodule.reflection_orthogonalComplement_singleton_eq_neg, summable_ofReal, LinearIsometryEquiv.reflections_generate_dim_aux, Complex.orthonormalBasisOneI_repr_apply, conj_mul, Matrix.LE.le.posSemidef, Affine.Triangle.dist_circumcenter_reflection_orthocenter, MeasureTheory.norm_condExpL2_coe_le, MeasureTheory.setLIntegral_nnnorm_condExpL2_indicator_le, MeasureTheory.mem_lpMeas_iff_aestronglyMeasurable, InnerProductSpace.trace_rankOne, imLm_coe, LinearMap.IsSymmetric.isSelfAdjoint, SchwartzMap.fourierMultiplierCLM_sum, NormedSpace.eq_iff_forall_dual_eq, ContinuousLinearEquiv.integral_comp_comm, continuousOn_cfcβ, Submodule.isIdempotentElem_starProjection, sum_mul_eq_sub_integral_mul', div_im, LinearEquiv.isometryOfOrthonormal_toLinearEquiv, hasFDerivAt_norm_rpow, dist_birkhoffAverage_apply_birkhoffAverage, IsSelfAdjoint.isClosed, LinearIsometry.inner_map_map, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, ClosedSubmodule.orthogonal_le, Submodule.orthogonalProjection_mem_subspace_orthogonalComplement_eq_zero, sum_inner, ofReal_mul, RKHS.kerFun_apply, im_to_real, instContinuousMapUniqueHom, ContinuousLinearMap.IsPositive.conj_adjoint, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, Submodule.IsCompl.projection_isSymmetricProjection_of_isOrtho, InnerProductSpace.Core.inner_neg_right, ContinuousLinearMap.isPositive_id, conjCLE_coe, contDiffOn_stereoToFun, ext_iff, Matrix.IsHermitian.trace_eq_sum_eigenvalues, Unitary.coe_symm_linearIsometryEquiv_apply, hasStrictFDerivAt_exp_smul_const', Matrix.posDef_gram_of_linearIndependent, range_cfcβ, LinearMap.adjoint_rTensor, MeasureTheory.convolution_assoc, hasGradientAt_iff_isLittleO_nhds_zero, normSq_inv, LinearMap.IsPositive.add, HilbertBasis.hasSum_orthogonalProjection, ContinuousLinearMap.isUnit_of_forall_le_norm_inner_map, LinearMap.adjoint_inner_right, MeasureTheory.mem_lpMeas_indicatorConstLp, InnerProductSpace.adjoint_rankOne, stereoInvFun_apply, InnerProductSpace.rankOne_eq_zero, IsGreatest.nnnorm_cfc, mul_wInner_left, TensorProduct.ext_iff_inner_left_threefold', Convex.toWeakSpace_closure, Submodule.isOrtho_sSup_right, LinearIsometry.lTensor_apply, ClosedSubmodule.bot_orthogonal_eq_top, Submodule.norm_sq_eq_add_norm_sq_starProjection, re_eq_norm_of_mul_conj, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_deriv_le, InnerProductSpace.inner_right_rankOne_apply, HilbertBasis.hasSum_repr, HasFDerivWithinAt.hasGradientWithinAt, IsSelfAdjoint.hasEigenvector_of_isMaxOn, innerSL_inj, MeasureTheory.condExpIndSMul_smul, Orthonormal.equiv_symm, TensorProduct.ext_iff_inner_left_threefold, MeasureTheory.lintegral_nnnorm_condExpL2_le, LinearMap.IsSymmetric.toLinearMap_symm, conj_eq_iff_re, StrongDual.toLp_of_not_memLp, AffineSubspace.signedInfDist_eq_signedDist_of_mem, LinearMap.IsSymmetric.coe_toSelfAdjoint, gaugeSeminorm_ball_one, TensorProduct.inner_lid_lid, EuclideanSpace.volume_closedBall_fin_two, OrthonormalBasis.toBasis_map, Matrix.piLp_ofLp_toEuclideanLin, cfcβAux_id, LinearMap.IsSymmetric.diagonalization_symm_apply, maximal_orthonormal_iff_basis_of_finiteDimensional, TensorProduct.norm_comm, rank_le_two, curveIntegral_segment_const, instMulPosReflectLE, ContinuousLinearMap.isPositive_toLinearMap_iff, Affine.Simplex.signedInfDist_apply_self, ConvexOn.sSup_of_countable_affine_eq, reCLM_coe, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, ofNat_mul_re, OrthonormalBasis.tensorProduct_repr_tmul_apply', ContinuousLinearMap.norm_map_of_mem_unitary, HasDerivWithinAt.inner, DifferentiableAt.inner, NormedSpace.exp_continuousMap_eq, MeasureTheory.hasFDerivAt_convolution_right_with_param, InnerProductSpace.exists_of_rankOne_eq_rankOne, InnerProductSpace.Core.inner_im_symm, OrthonormalBasis.sum_sq_norm_inner_right, SchwartzMap.postcompCLM_apply, LinearIsometryEquiv.reflections_generate, AffineSubspace.signedInfDist_eq_signedDist_orthogonalProjection, Submodule.map_orthogonal_equiv, isUniformEmbedding_ofReal, EuclideanSpace.coe_proj, Convex.norm_image_sub_le_of_norm_hasDerivWithin_le, Matrix.l2_opNNNorm_mulVec, cfcβ_mem_elemental, Orthonormal.inner_left_right_finset, HasCompactSupport.hasFDerivAt_convolution_right, SchwartzMap.lineDerivOp_compCLMOfContinuousLinearEquiv, ClosedSubmodule.top_orthogonal_eq_bot, EuclideanGeometry.reflection_reflection, Submodule.norm_orthogonalProjection_apply_le, Finsupp.inner_sum, conj_I_ax, nnnorm_nnratCast, HasFDerivWithinAt.inner, TensorProduct.norm_assoc, TensorProduct.nnnorm_tmul, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, I_eq_zero_or_im_I_eq_one, InnerProductSpace.toDualMap_apply, LinearMap.IsSymmetric.iSup_iInf_eq_top_of_commute, LinearMap.IsSymmetric.adjoint_conj, normSq_nonneg, Orthonormal.inner_products_summable, InnerProductSpace.gramSchmidt_orthogonal, ContinuousLinearMap.adjoint_inner_left, TensorProduct.inner_mapIncl_mapIncl, InnerProductSpace.gramSchmidt_pairwise_orthogonal, le_iff_re_im, InnerProductSpace.AlgebraOfCoalgebra.mul_def, Matrix.l2_opNorm_diagonal, LinearMap.extendToπ_apply, cfcHom_integral, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, Affine.Simplex.orthogonalProjectionSpan_congr, ContDiffAt.hasStrictFDerivAt', Affine.Simplex.mongePlane_def, ProbabilityTheory.complexMGF_id_mul_I, Matrix.isSymmetric_toEuclideanLin_iff, ProbabilityTheory.map_pi_eq_stdGaussian, inner_neg_right, ContinuousLinearMap.IsPositive.isSymmetric, nnnorm_apply_le_nnnorm_cfcβ, Orthonormal.isHilbertSum, OrthonormalBasis.singleton_apply, OrthonormalBasis.equiv_apply, uniqueNonUnitalContinuousFunctionalCalculus, SchwartzMap.lineDeriv_eq_fourierMultiplierCLM, sqrt_one, inner_eq_sum_norm_sq_div_four, MeasureTheory.lpMeasToLpTrimLie_symm_indicator, LinearMap.IsSymmetric.restrict_invariant, LinearMap.isometryOfInner_toLinearMap, ContinuousLinearMap.rayleighQuotient_zero_apply, LinearIsometryEquiv.conjStarAlgEquiv_trans, LinearMap.adjoint_comp_self_injective_iff, LinearMap.IsSymmetric.continuous, ContinuousMap.ideal_isMaximal_iff, integral_conj, LinearIsometry.extend_apply, InnerProductSpace.rank_rankOne, LinearMap.isSymmetric_sum, Module.Basis.coe_toOrthonormalBasis_repr_symm, geometric_hahn_banach_of_nonempty_interior', Submodule.isOrtho_top_left, IsometricContinuousFunctionalCalculus.toNonUnital, InnerProductSpace.toDual_apply_apply, Matrix.PosSemidef.eigenvalues_nonneg, exists_norm_eq_mul_self, Affine.Simplex.vectorSpan_isOrtho_altitude_direction, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.nonneg_iff_isPositive, real_smul_eq_coe_smul, OrthogonalFamily.isInternal_iff, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, measurable_re, Submodule.linearEquiv_det_reflection, LinearMap.isSymmetric_linearIsometryEquiv_conj_iff, ProperCone.innerDual_singleton, real_inner_eq_re_inner, nnnorm_ofNat, add_conj, Submodule.IsOrtho.map, EuclideanGeometry.reflection_eq_self_iff, ofReal_re_ax, differentiable_inner, InnerProductSpace.Core.inner_self_eq_norm_mul_norm, CFC.exp_eq_normedSpace_exp, im_eq_conj_sub, LDL.lower_conj_diag, hasFDerivAt_integral_of_dominated_loc_of_lip', Submodule.toLinearMap_starProjection_eq_isComplProjection, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, RKHS.kerFun_dense, InnerProductSpace.rankOne_def, TensorProduct.nnnorm_map, InnerProductSpace.Core.inner_self_eq_zero, LinearMap.singularValues_eq_zero_iff, conj_im_ax, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, SchwartzMap.convolution_apply, Submodule.sub_starProjection_mem_orthogonal, inner_self_conj, dist_birkhoffAverage_birkhoffAverage, LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, OrthonormalBasis.repr_apply_apply, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, ContinuousLinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range, integrable_cfcβ, Matrix.l2_opNNNorm_conjTranspose, ofReal_add, ClosedSubmodule.orthogonal_eq_inter, EuclideanGeometry.Sphere.orthogonalProjection_orthRadius_center, MeasureTheory.L2.integral_inner_eq_sq_eLpNorm, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed, SchwartzMap.compCLMOfAntilipschitz_apply, SchwartzMap.fourierInv_apply_eq, LinearIsometryEquiv.conjStarAlgEquiv_refl, CurveIntegrable.fun_zero, MeasureTheory.L2.inner_indicatorConstLp_one, ofReal_neg, MeasureTheory.L2.inner_indicatorConstLp_indicatorConstLp, Matrix.PosSemidef.nonneg, LinearMap.IsSymmetric.toSelfAdjoint_apply, conj_div, EuclideanSpace.edist_single_same, EuclideanGeometry.orthogonalProjection_subtype, ofReal_zpow, im_mul_ofReal, Submodule.coe_orthogonalDecomposition, EuclideanGeometry.two_zsmul_oangle_self_orthogonalProjection, HasDerivAtFilter.hasGradientAtFilter, Submodule.finrank_orthogonal_span_singleton, Matrix.nonneg_iff_posSemidef, summable_conj, geometric_hahn_banach_point_point, norm_cfcβ_lt_iff, wInner_zero_right, LinearMap.isPositive_natCast, inner_smul_real_right, TensorProduct.toLinearEquiv_congrIsometry, LinearMap.injective_iff_forall_lt_finrank_singularValues_pos, hasFDerivAt_exp_smul_const', Submodule.isOrtho_iSup_left, IsCoercive.bounded_below, SchwartzMap.postcompCLM_postcompCLM, Commute.cfcβHom, Submodule.mem_orthogonal', LinearMap.toMatrixOrthonormal_symm_apply, ContinuousLinearMap.IsStarNormal.orthogonal_range, DirectSum.IsInternal.collectedBasis_orthonormal, Matrix.posDef_gram_iff_linearIndependent, wInner_sub_left, LinearMap.toMatrix_innerββ_apply, Matrix.permMatrix_l2_opNorm_le, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, ContinuousLinearMap.IsIdempotentElem.TFAE, TensorProduct.toLinearEquiv_commIsometry, wInner_one_eq_inner, IsRCLikeNormedField.out, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, Submodule.norm_sq_eq_add_norm_sq_projection, LinearMap.extendToπ'_apply_re, inner_zero_left, re_to_real, Submodule.orthogonal_gc, Matrix.inner_toEuclideanCLM, EuclideanGeometry.orthogonalProjection_vadd_eq_self, neg_iff, ClosedSubmodule.orthogonal_orthogonal_monotone, curveIntegral_restrictScalars, Matrix.PosSemidef.toLinearMapβ'_zero_iff, Submodule.starProjection_isSymmetric, sqrt_eq_real_add_ite, Submodule.starProjection_apply, Submodule.reflection_mem_subspace_orthogonal_precomplement_eq_neg, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv', inv_im, Matrix.l2_opNorm_conjTranspose, ProbabilityTheory.IndepFun.integral_fun_mul_eq_mul_integral, ContinuousLinearMap.rayleighQuotient_add, Matrix.instNonnegSpectrumClass, LinearMap.isSelfAdjoint_iff', ofReal_prod, contDiffAt_euclidean, innerSLFlip_apply_apply, ofReal_mul_pos_iff, Affine.Triangle.dist_orthocenter_reflection_circumcenter, OrthogonalFamily.hasSum_linearIsometry, ofReal_finsupp_sum, finrank_euclideanSpace, EuclideanGeometry.oangle_orthogonalProjection_self, LinearMap.IsPositive.isSelfAdjoint, InnerProductSpaceable.inner_.norm_sq, Submodule.top_orthogonal_eq_bot, ConvexOn.sSup_of_nat_affine_eq, Orthonormal.equiv_trans, Submodule.fst_orthogonalDecomposition_apply, HilbertBasis.dense_span, inner_add_left, Submodule.orthogonal_orthogonal_eq_closure, Submodule.smul_starProjection_singleton, one_im, toZeroLEOneClass, with_gaugeSeminormFamily, TensorProduct.ext_iff_inner_right, natCast_re, LinearEquiv.isPositive_symm_iff, InnerProductSpace.enorm_rankOne, InnerProductSpace.Core.inner_self_nonneg, Orthonormal.inner_finsupp_eq_sum_right, ofReal_finsuppProd, InnerProductSpace.continuousLinearMapOfBilin_zero, Convex.exists_forall_hasDerivWithinAt, inner_re_symm, ContinuousLinearMap.toLinearMap_innerSL_apply, WithLp.volume_preserving_toLp, Submodule.orthogonalFamily_self, SchwartzMap.fourierMultiplierCLM_apply, EuclideanGeometry.dist_orthogonalProjection_eq_dist_iff_eq_of_mem, ClosedSubmodule.mem_symplComp_iff, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_norm_quasispectrum, LinearMap.IsSymmetric.adjoint_eq, IsSelfAdjoint.dense_domain, LinearMap.isPositive_sum, Submodule.starProjection_norm_le, contDiffOn_euclidean, HasGradientAt.hasFDerivAt, norm_le_re_iff_eq_norm, AffineSubspace.abs_signedInfDist_eq_dist_of_mem_affineSpan_insert, RKHS.inner_kerFun, PiLp.volume_preserving_ofLp, Real.fourier_fderiv, MeasureTheory.AEStronglyMeasurable.inner, Submodule.inner_orthogonalProjection_eq_of_mem_right, Submodule.reflection_reflection, ContinuousMap.adjoin_id_eq_span_one_union, SchwartzMap.instLineDerivSMul, Submodule.isOrtho_iff_le, MeasureTheory.condExp_smul, SchwartzMap.compSubConstCLM_zero, LinearPMap.adjoint_apply_of_not_dense, HasFDerivWithinAt.norm_sq, wInner_smul_right, CFC.abs_algebraMap, ordinaryHypergeometric_radius_top_of_neg_natβ, LinearMap.image_closure_of_convex, ClosedSubmodule.iInf_orthogonal, LinearMap.tracePositiveLinearMap_apply, EuclideanGeometry.reflection_apply_of_mem, Matrix.isHermitian_gram, integral_inner, ofReal_im, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, range_cfcβHom_le, StrongDual.extendRCLikeβ_apply, LinearMap.bound_of_ball_bound', LinearMap.isPositive_linearIsometryEquiv_conj_iff, ContinuousLinearMap.rayleighQuotient_le_of_norm_mem_resolventSet, Orthonormal.linearIsometryEquiv_symm_apply_single_one, Matrix.PosDef.commute_iff, OrthonormalBasis.equiv_self_rfl, Matrix.IsHermitian.roots_charpoly_eq_eigenvalues, Matrix.IsHermitian.cfcAux_apply, abs_im_le_norm, finrank_le_two, Matrix.IsHermitian.splits_charpoly, InnerProductSpace.coe_gramSchmidtBasis, MeasureTheory.integral_charFun_Icc, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, Submodule.reflection_inv, sum_mul_eq_sub_integral_mulβ', toCompleteSpace, nonneg_iff, LinearEquiv.image_closure_of_convex, Affine.Simplex.orthogonalProjection_circumcenter, ofReal_zero, Matrix.ofLp_toEuclideanCLM, summable_pow_div_add, Submodule.norm_starProjection, Filter.Tendsto.cfcβ, ClosedSubmodule.sup_orthogonal, LinearMap.IsSymmetric.orthogonalFamily_eigenspaces', hasDerivAt_exp_smul_const, ClosedSubmodule.sub_mem_orthogonal_of_inner_left, continuous_re, LinearPMap.adjoint_isClosed, Unitary.linearIsometryEquiv_coe_symm_apply, Submodule.eq_starProjection_of_mem_of_inner_eq_zero, exists_dual_vector, Orthonormal.map_equiv, LinearMap.IsSymmetric.hasEigenvalue_eigenvalues, ContinuousLinearMap.rayleighQuotient_le_norm, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, OrthonormalBasis.det_to_matrix_orthonormalBasis, instContinuousStar, Convex.lipschitzOnWith_of_nnnorm_hasDerivWithin_le, LinearMap.isPositive_toContinuousLinearMap_iff, OrthogonalFamily.summable_of_lp, AddChar.wInner_cWeight_eq_one_iff_eq, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, Affine.Simplex.exists_forall_dist_eq_iff_exists_excenterExists_and_eq_excenter, norm_inner_eq_norm_tfae, curveIntegral_fun_add, Submodule.isCompl_orthogonal_of_hasOrthogonalProjection, MeasureTheory.isTightMeasureSet_range_iff_tendsto_limsup_inner, sqrt_map, Submodule.reflection_mul_reflection, curveIntegral_fun_neg, zero_re, inner_tmul_eq, LinearPMap.IsFormalAdjoint.le_adjoint, Matrix.instFiniteElemRealSpectrum, InnerProductSpace.Core.inner_re_symm, inr_comp_cfcβHom_eq_cfcβAux, InnerProductSpace.gramSchmidt_triangular, Submodule.starProjection_map_apply, smul_im, LinearMap.star_eq_adjoint, Matrix.l2_opNNNorm_mul, tendsto_ofReal_cobounded_cobounded, differentiableWithinAt_euclidean, InnerProductSpace.Core.toNormedSpaceCore, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot', MeasureTheory.integral_prod_mul, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_exists_dist_eq, LinearPMap.adjointDomainMkCLM_apply, Matrix.isPositive_toEuclideanLin_iff, nnnorm_cfc_le_iff, TensorProduct.enorm_tmul, Polynomial.aeval_conj, Submodule.starProjection_bot, re_eq_add_conj, ContinuousLinearMap.isometry_iff_adjoint_comp_self, ContDiff.inner, HasGradientAt.differentiableAt, ContDiffAt.hasStrictFDerivAt, InnerProductSpace.gramSchmidtOrthonormalBasis_apply_of_orthogonal, TemperedDistribution.fourierMultiplierCLM_toTemperedDistributionCLM_eq, Submodule.orthogonal_closure, LinearMap.IsSymmetric.orthogonalFamily_eigenspace_inf_eigenspace, IsSelfAdjoint.conj_adjoint, TensorProduct.inner_assoc_assoc, InnerProductSpace.Core.norm_inner_le_norm, EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eq, ContinuousLinearMap.reApplyInnerSelf_apply, Affine.Simplex.direction_mongePlane, wInner_const_left, LinearMap.IsIdempotentElem.isSymmetric_iff_isOrtho_range_ker, wInner_cWeight_const_left, LinearMap.IsSymmetric.coe_reApplyInnerSelf_apply, LinearMap.le_def, MeasureTheory.integral_condExpL2_eq_of_fin_meas_real, EuclideanSpace.toLp_single, inner_self_eq_norm_mul_norm, hasStrictFDerivAt_norm_sq, Submodule.starProjection_unit_singleton, LinearMap.adjoint_toSpanSingleton, Matrix.IsHermitian.sort_roots_charpoly_eq_eigenvaluesβ, OrthonormalBasis.coe_toBasis, Submodule.reflection_sub, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_radius_nonneg_and_vsub_mem_and_norm_sq, inner_apply, LinearMap.IsSymmetric.natCast, ClosedSubmodule.mem_orthogonal, LinearEquiv.coe_isometryOfInner, Matrix.posDef_iff_eq_conjTranspose_mul_self, MeasureTheory.condExpIndL1_smul', LinearMap.re_inner_adjoint_mul_self_nonneg, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, RKHS.coeCLM_injective, MeasureTheory.Integrable.re_im_iff, normSq_mul, LinearMap.isPositive_self_comp_adjoint, ContinuousLinearMap.ker_self_comp_adjoint, hasSum_conj, circleIntegral.integral_smul, hasDerivAt_integral_of_dominated_loc_of_deriv_le, orthonormal_subtype_iff_ite, ProbabilityTheory.IndepFun.integral_fun_comp_mul_comp, ContinuousLinearMap.instStarModuleId, wInner_smul_left, continuous_cfcHomSuperset_left, EuclideanGeometry.orthogonalProjection_affineSpan_singleton, LinearIsometryEquiv.toLinearEquiv_lTensor, Matrix.linearIndependent_of_posDef_gram, exists_dual_vector'', ContDiffAt.contDiffAt_implicitFunction, LinearIsometry.adjoint_comp_self', norm_wInner_le, Continuous.cfc_of_mem_nhdsSet, LinearIsometryEquiv.toLinearEquiv_smul, Module.Dual.extendRCLikeβ_apply, curveIntegralFun_neg, binomialSeries_radius_eq_top_of_nat, LinearMap.IsSymmetric.eigenvectorBasis_apply_self_apply, Matrix.l2_opNNNorm_def, HasGradientAtFilter.isBigO_sub, ContinuousLinearMap.adjointAux_adjointAux, Measurable.im, Submodule.coe_inner, hasDerivAt_exp, Submodule.orthogonalProjection_apply_eq_linearProjOfIsCompl, norm_im_le_norm, UniformSpace.Completion.Continuous.inner, MeasureTheory.condExpL2_indicator_of_measurable, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_eq_bot, inner_zero_right, LinearMap.eq_adjoint_iff, inner_self_eq_zero, Orthonormal.equiv_toLinearEquiv, cfc_integral, MeasureTheory.AEStronglyMeasurable.const_inner, EuclideanGeometry.dist_sq_eq_dist_orthogonalProjection_sq_add_dist_orthogonalProjection_sq, Orthonormal.inner_right_finsupp, ConvexOn.convex_re_epigraph, LinearMap.norm_extendToπ'_apply_sq, OrthonormalBasis.tensorProduct_apply', EuclideanSpace.basisFun_repr, sqrt_of_nonneg, ContinuousLinearMap.integral_comp_id_comm', SchwartzMap.integral_pow_mul_iteratedFDeriv_le, inner_product_apply_eigenvector, realLinearIsometryEquiv_symm_apply, InnerProductSpace.gramSchmidtOrthonormalBasis_det, OrthonormalBasis.sum_sq_norm_inner_left, LinearMap.isPositive_iff_complex, inner_self_eq_norm_sq, ContinuousLinearMap.isSelfAdjoint_iff', Submodule.sndL_comp_coe_orthogonalDecomposition, OrthonormalBasis.equiv_apply_euclideanSpace, continuous_ofReal, exists_norm_mul_eq_self, stereographic_neg_apply, isSelfAdjoint_starProjection, InnerProductSpace.gramSchmidt_def', MeasureTheory.condExpL2_indicator_eq_toSpanSingleton_comp, lipschitzWith_re, Measurable.re, ofReal_pow, OrthonormalBasis.det_adjustToOrientation, SchwartzMap.fourierMultiplierCLM_ofReal, InnerProductSpace.Core.inner_smul_ofReal_left, Complex.orthonormalBasisOneI_repr_symm_apply, ContinuousLinearMap.orthogonalComplement_iSup_eigenspaces_eq_bot, LocallyConvexSpace.toPolynormableSpace, curveIntegralFun_fun_zero, ofReal_alg, tendsto_sum_mul_atTop_nhds_one_sub_integralβ, Submodule.sInf_orthogonal, LinearMap.IsSymmetric.directSum_isInternal_of_commute, OrthonormalBasis.inner_eq_zero, curveIntegralFun_def', MeasureTheory.instCompleteSpaceSubtypeAEEqFunMemAddSubgroupLpSubmoduleLpMeasOfFactLeMeasurableSpace, Submodule.isOrtho_span, ContinuousLinearMap.norm_extendToπ'_bound, MeasureTheory.AEStronglyMeasurable.re, ContinuousMultilinearMap.integral_apply, MeasureTheory.lintegral_nnnorm_condExpL2_indicator_le_real, conj_tsum, HasGradientWithinAt.fderivWithin_apply, inner_add_add_self, sum_mul_eq_sub_integral_mulβ, I_im, complexLinearIsometryEquiv_symm_apply, ContinuousLinearMap.le_def, hasGradientAt_iff_tendsto, InnerProductSpace.Core.inner_sub_sub_self, LinearMap.isPositive_zero, MeasureTheory.contDiffOn_convolution_right_with_param_comp, RKHS.coeCLM_apply, ContinuousLinearMap.IsPositive.re_inner_nonneg_left, MeasureTheory.ProbabilityMeasure.tendsto_iff_forall_integral_rclike_tendsto, StrongDual.extendRCLikeβα΅’_symm_apply, Matrix.PosSemidef.kronecker, inner_add_right, LinearIsometry.orthonormal_comp_iff, continuous_inner, sqrt_neg_one, ContinuousLinearMap.IsStarProjection.ext_iff, nnnorm_inner_le_nnnorm, NonUnitalIsometricContinuousFunctionalCalculus.isGreatest_nnnorm_quasispectrum, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, InnerProductSpace.Core.inner_zero_right, IsometricContinuousFunctionalCalculus.nnnorm_spectrum_le, wInner_const_right, InnerProductSpace.rankOne_def', EuclideanGeometry.eq_or_eq_reflection_of_dist_eq, Submodule.isClosed_orthogonal, EuclideanSpace.norm_eq, isCauSeq_norm, Matrix.IsHermitian.eigenvectorUnitary_apply, ContinuousOn.cfc_of_mem_nhdsSet, ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero, SchwartzMap.fourierMultiplierCLM_const, Submodule.norm_orthogonalProjection_apply, ContinuousLinearMap.IsPositive.inner_nonneg_left, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, HasFDerivAt.inner, MeasureTheory.L2.eLpNorm_inner_lt_top, LinearMap.adjoint_lTensor, EuclideanGeometry.orthogonalProjection_vadd_smul_vsub_orthogonalProjection, conj_eq_iff_real, LinearMap.singularValues_pos_iff_lt_finrank_range, norm_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul, OrthonormalBasis.map_apply, ofNat_mul_im, LinearMap.toMatrixOrthonormal_apply, MeasureTheory.condExpL1CLM_lpMeas, Submodule.isSymmetricProjection_starProjection, Submodule.eq_starProjection_of_mem_orthogonal, Matrix.IsHermitian.det_eq_prod_eigenvalues, OrthogonalFamily.inner_sum, LinearMap.IsPositive.smul_of_nonneg, cfcβAux_injective, ClosedSubmodule.mem_orthogonal_toSubmodule_iff, EuclideanSpace.inner_eq_star_dotProduct, LinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range, Matrix.IsHermitian.spectrum_eq_image_range, MeasureTheory.convolution_assoc', OrthonormalBasis.sum_repr_symm, isCauSeq_im, InnerProductSpace.norm_sq_eq_re_inner, Affine.Simplex.orthogonalProjectionSpan_faceOpposite_eq_point_rev, Orthonormal.inner_left_sum, StrongDual.extendRCLikeβ_symm_apply, Pi.orthonormalBasis.toBasis, LinearIsometry.map_starProjection, Orientation.inner_mul_areaForm_sub', inner_sub_left, Matrix.posSemidef_gram, ContinuousLinearMap.isSelfAdjoint_toLinearMap_iff, LinearMap.singularValues_fin, EuclideanGeometry.dist_orthogonalProjection_eq_infNndist, Submodule.inf_orthogonal, LinearMap.sq_singularValues_of_lt, InnerProductSpace.innerSL_norm, hasFDerivAt_exp_zero, toWeakSpace_closedConvexHull_eq, cfcβ_mem, Submodule.IsOrtho.le, Submodule.reflection_map, InnerProductSpace.span_gramSchmidt_Iic, LinearMap.IsSymmetric.direct_sum_isInternal, Submodule.det_reflection, hasSum_re, TensorProduct.inner_comm_comm, Submodule.inner_orthogonalProjection_eq_of_mem_left, ContinuousLinearMap.extendToπ_apply, ContinuousLinearMap.IsPositive.add, EuclideanSpace.volume_ball_fin_three, InnerProductSpace.laplacianWithin_eq_iteratedFDerivWithin_stdOrthonormalBasis, CurveIntegrable.fun_neg, ContinuousLinearMap.norm_extendToπ', Submodule.inner_left_of_mem_orthogonal, linearIndependent_of_ne_zero_of_inner_eq_zero, MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner, LinearPMap.isSelfAdjoint_def, DirectSum.IsInternal.subordinateOrthonormalBasis_def, SchwartzMap.compSubConstCLM_comp, IsContDiffImplicitAt.bijective, Submodule.eq_starProjection_of_mem_orthogonal', ProbabilityTheory.covarianceBilin_apply_basisFun, hasGradientAt_iff_hasFDerivAt, LinearMap.IsSymmetric.invariant_orthogonalComplement_eigenspace, Submodule.toLinearMap_orthogonalProjection_eq_linearProjOfIsCompl, curveIntegrable_neg_iff, LinearMap.finrank_range_adjoint, maximal_orthonormal_iff_orthogonalComplement_eq_bot, Submodule.reflection_orthogonal, LinearEquiv.isometryOfInner_toLinearEquiv, inner_eq_zero_of_left, LinearMap.sq_singularValues_fin, MeasureTheory.iteratedDeriv_charFun, ContinuousLinearMap.adjoint_comp_self_injective_iff, Submodule.isOrtho_top_right, LinearMap.IsSymmetric.smul, HilbertBasis.repr_symm_single, HilbertBasis.repr_apply_apply, TensorProduct.assocIsometry_apply, Matrix.toLin_conjTranspose, instStarModuleReal, Orthonormal.inner_finsupp_eq_sum_left, LinearMap.range_adjoint_comp_self, Matrix.IsHermitian.spectral_theorem, ContDiffAt.hasStrictFDerivAt_implicitFunction, integrableOn_cfcβ, norm_cfcβ_le, mul_im_I_ax, continuous_conj, ImplicitFunctionData.contDiffAt_implicitFunction, EuclideanGeometry.dist_reflection_eq_of_mem, LinearIsometryEquiv.rTensor_apply, LinearIsometryEquiv.inner_map_map, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangent, InnerProductSpace.isStarProjection_rankOne_self, norm_natCast, coord_norm', DirectSum.IsInternal.collectedOrthonormalBasis_mem, contDiffAt_inner, LinearIsometry.integral_comp_comm, OrthonormalBasis.measurePreserving_repr_symm, lp.summable_inner, spec_cfcβAux, MeasureTheory.measureReal_abs_gt_le_integral_charFun, DifferentiableOn.inner, ClosedSubmodule.orthogonal_eq_top_iff, StrongDual.extendRCLikeβα΅’_apply, EuclideanSpace.piLpCongrLeft_single, Submodule.sup_orthogonal_inf_of_hasOrthogonalProjection, Submodule.inner_right_of_mem_orthogonal, hasFDerivAt_exp_smul_const, Differentiable.inner, LinearMap.IsPositive.trace_nonneg, EuclideanGeometry.dist_reflection, PreInnerProductSpace.Core.re_inner_nonneg, ofReal_intCast, InnerProductSpaceable.add_left, complexRingEquiv_symm_apply, Matrix.IsHermitian.instContinuousFunctionalCalculusIsClosedEmbedding, normSq_eq_def', integrable_cfcβ', ofReal_eq_zero, ContinuousLinearMap.self_comp_adjoint_injective_iff, hasFDerivWithinAt_euclidean, ClosedSubmodule.mem_orthogonal_iff, EuclideanGeometry.orthogonalProjection_eq_orthogonalProjection_iff_vsub_mem, HasCompactSupport.contDiff_convolution_left, Matrix.PosDef.isStrictlyPositive, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_blockTriangular, re_mul_ofReal, nnnorm_cfc_le, LinearMap.IsSymmetricProjection.hasOrthogonalProjection_range, Submodule.starProjection_orthogonal, ContinuousLinearMap.instNonnegSpectrumClassRealId, ContinuousLinearMap.IsIdempotentElem.isPositive_iff_isSelfAdjoint, ContinuousMap.setOfIdeal_eq_compl_singleton, ContinuousLinearMap.integral_comp_commSL, ofRealCLM_norm, Matrix.IsHermitian.eigenvectorUnitary_coe, Complex.sqrt_map, stereographic_target, inner_self_ofReal_norm, integrable_cfc', Unitary.norm_map, LinearMap.instStarModuleId, linearIndependent_of_ne_zero_of_wInner_cWeight_eq_zero, Submodule.starProjection_apply_mem, StarAlgEquiv.eq_linearIsometryEquivConjStarAlgEquiv, LinearIsometryEquiv.symm_conjStarAlgEquiv_apply_apply, im_tsum, InnerProductSpace.rankOne_comp_rankOne, EuclideanGeometry.dist_eq_iff_dist_orthogonalProjection_eq, Matrix.PosSemidef.det_nonneg, ProbabilityTheory.charFun_inv_sqrt_mul_sum, parallelogram_law, Submodule.orthogonal_closure', LinearIsometry.toLinearMap_rTensor, nnnorm_apply_le_nnnorm_cfc, norm_re_le_norm, Matrix.toEuclideanLin_eq_toLin, Matrix.isHermitian_iff_isSymmetric, re_inner_self_pos, Continuous.cfc, Matrix.PosSemidef.inv_sqrt, Matrix.IsHermitian.cfcHom_eq_cfcAux, convex_RCLike_iff_convex_real, Submodule.le_orthogonal_iff_le_orthogonal, curveIntegral_zero, Matrix.finite_real_spectrum, InnerProductSpace.laplacian_eq_iteratedFDeriv_stdOrthonormalBasis, Submodule.IsOrtho.comap_iff, InnerProductSpace.rankOne_comp, Convex.exists_forall_hasFDerivWithinAt_of_fderivWithin_symmetric, inner_eq_neg_one_iff_of_norm_eq_one, Submodule.mem_orthogonal, exists_dual_vector', EuclideanSpace.basisFun_inner, LinearMap.IsSymmetric.iSup_iSup_eigenspace_inf_eigenspace_eq_top_of_commute, intervalIntegral.hasFDerivAt_integral_of_dominated_of_fderiv_le, MeasureTheory.integrable_condExpL2_of_isFiniteMeasure, inner_smul_right, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, EuclideanSpace.ofLp_single, LinearMap.polar_AbsConvex, differentiableAt_euclidean, EuclideanGeometry.dist_orthogonalProjection_eq_infDist, OrthonormalBasis.reindex_toBasis, nonneg_iff_exists_ofReal, geometric_hahn_banach_open, EuclideanGeometry.orthogonalProjection_mem, conj_wInner_symm, InnerProductSpace.isSymmetric_rankOne_self, ofReal_expect, Commute.cfcHom, inner_eq_one_iff_of_norm_eq_one, Asymptotics.isBigO_atTop_natCast_rpow_of_tendsto_div_rpow, LinearIsometryEquiv.symm_rTensor, LinearMap.isSymmetricProjection_iff, Affine.Simplex.orthogonalProjectionSpan_restrict, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, cfc_apply_mem_elemental, TensorProduct.commIsometry_symm, isStarProjection_starProjection, unitary.norm_map, ofReal_nonpos, SchwartzMap.tsupport_fderivCLM_subset, MeasureTheory.Integrable.inner_const, ContinuousLinearMap.integral_comp_L1_comm, curveIntegralFun_add, range_cfcβ_subset, Matrix.isSymmetric_toLin_iff, LinearEquiv.isSymmetric_symm_iff, InnerProductSpace.gramSchmidt_def'', ContinuousLinearMap.intervalIntegral_apply, OrthonormalBasis.equiv_symm, nnnorm_cfcβHom, EuclideanSpace.volume_preserving_symm_measurableEquiv_toLp, InnerProductSpace.Core.inner_mul_symm_re_eq_norm, MeasureTheory.integral_fin_nat_prod_eq_prod, OrthonormalBasis.orthonormal_adjustToOrientation, Continuous.inner_, ContinuousOn.cfcβ, inv_pos_of_pos, curveIntegralFun_sub, ofReal_one, toIsOrderedAddMonoid, OrthogonalFamily.eq_ite, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, Continuous.inner, Matrix.IsHermitian.exists_eigenvector_of_ne_zero, re_le_re, differentiableOn_euclidean, reLm_coe, Convex.norm_image_sub_le_of_norm_deriv_le, SchwartzMap.convolution_continuous_left, ContinuousLinearMap.adjoint_toSpanSingleton, InnerProductSpace.mem_span_gramSchmidt, inner_smul_real_left, natCast_im, MeasureTheory.integrable_condExpL2_indicator, WithLp.volume_preserving_symm_measurableEquiv_toLp_prod, MeasureTheory.MemLp.re, EuclideanGeometry.dist_orthogonalProjection_eq_zero_iff, Submodule.sub_mem_orthogonal_of_inner_right, nnnorm_conj, ratCast_re, MeasureTheory.AEStronglyMeasurable.im, cfc_comp_norm, ofReal_eq_re_of_isSelfAdjoint, EuclideanGeometry.dist_sq_smul_orthogonal_vadd_smul_orthogonal_vadd, Matrix.IsHermitian.coe_re_apply_self, MeasureTheory.Integrable.re, range_mfderiv_coe_sphere, RKHS.kerFun_inner, ofReal_div, HasFDerivWithinAt.curveIntegral_segment_source, ClosedSubmodule.inf_orthogonal_eq_bot, NormedSpace.isCompact_closure_of_isBounded, Submodule.reflection_eq_self_iff, Orthonormal.equiv_refl, stereographic_source, integral_coe_re_add_coe_im, wInner_one_const_right, Commute.cfc, lt_iff_re_im, IsometricContinuousFunctionalCalculus.norm_spectrum_le, Matrix.posSemidef_iff_eq_sum_vecMulVec, ContinuousLinearMap.ker_adjoint_comp_self, ConvexOn.univ_sSup_affine_eq, Matrix.ofLp_toEuclideanLin_apply, ContinuousOn.cfcβ_of_mem_nhdsSet, SchwartzMap.integralCLM_apply, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, norm_two, EuclideanGeometry.exists_dist_eq_iff_exists_dist_orthogonalProjection_eq, LinearMap.IsSymmetric.apply_eigenvectorBasis, EuclideanSpace.volume_ball_fin_two, DirectSum.IsInternal.card_filter_subordinateOrthonormalBasisIndex_eq, im_eq_zero_of_le, norm_add_sq, Submodule.finrank_add_inf_finrank_orthogonal', norm_sq_re_conj_add, NormedSpace.polar_ball, HasFTaylorSeriesUpToOn.hasStrictFDerivAt, EuclideanSpace.inner_basisFun_real, innerSLFlip_apply, EuclideanGeometry.Sphere.IsTangentAt.eq_orthogonalProjection, Submodule.ker_starProjection, sqrt_neg_I, InnerProductSpace.toContinuousLinearMap_toDualMap, MeasureTheory.MemLp.condExpL2_ae_eq_condExp', normSq_pos, InnerProductSpace.Core.inner_sub_left, Affine.Triangle.dist_circumcenter_reflection_orthocenter_finset, MeasureTheory.taylorWithinEval_charFun_two_zero, ProbabilityTheory.iIndepFun.integral_prod_eq_prod_integral, IsSelfAdjoint.commute_cfcβHom, inner_eq_ofReal_norm_sq_left_iff, norm_add_mul_self, LinearIsometryEquiv.symm_conjStarAlgEquiv, Submodule.topologicalClosure_eq_top_iff, conj_im, Function.RCLike.hasTemperateGrowth_ofReal, MeasureTheory.Integrable.ofReal, EuclideanSpace.volume_ball, LinearMap.IsSymmetric.zero, TensorProduct.enorm_assoc, conj_I, LinearMap.coe_isometryOfInner, OrthonormalBasis.repr_symm_single, contDiff_inner, cfcL_integral, Submodule.reflection_bot, innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, IsContDiffImplicitAt.contDiffAt, InnerProductSpace.Core.inner_self_ofReal_re, ContinuousLinearMap.isPositive_def', LinearMap.adjoint_inner_left, Matrix.frobenius_norm_mul, Matrix.star_dotProduct_gram_mulVec, hasStrictFDerivAt_exp_zero, hasSum_iff, measurable_im, Matrix.IsHermitian.spectrum_real_eq_range_eigenvalues, curveIntegral_eq_intervalIntegral_deriv, inv_def, sqrt_I, Matrix.PosDef.kronecker, OrthogonalFamily.range_linearIsometry, EuclideanGeometry.reflection_eq_iff_orthogonalProjection_eq, Submodule.ker_orthogonalProjection, locallyIntegrableOn_mul_sum_Icc, LinearMap.IsSymmetric.hasEigenvalue_iInf_of_finiteDimensional, innerSL_real_flip, Submodule.reflection_map_apply, nnnorm_two, TensorProduct.dist_tmul_le, SchwartzMap.integral_smul_lineDerivOp_right_eq_neg_left, re_eq_ofReal_of_isSelfAdjoint, NormedSpace.isEmbedding_inclusionInDoubleDualWeak, Submodule.sup_orthogonal_of_hasOrthogonalProjection, MeasureTheory.L2.inner_indicatorConstLp_one_indicatorConstLp_one, TensorProduct.norm_lid, MeasureTheory.lpTrimToLpMeas_ae_eq, MeasureTheory.charFun_eq_charFunDual_toDualMap, Matrix.instIsOrderedAddMonoid, CFC.quasispectrum_abs, Submodule.starProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_iSup_right, TensorProduct.toLinearEquiv_assocIsometry, Submodule.IsOrtho.inner_eq, Submodule.IsOrtho.disjoint, norm_cfc_le, SchwartzMap.compCLM_apply, EuclideanGeometry.orthogonalProjection_orthogonalProjection, norm_nnratCast, toMatrix_innerSL_apply, OrthonormalBasis.equiv_apply_basis, ClosedSubmodule.sInf_orthogonal, Matrix.PosSemidef.re_dotProduct_nonneg, Orientation.volumeForm_robust', EuclideanGeometry.orthogonalProjection_vsub_mem_direction, Submodule.HasOrthogonalProjection.exists_orthogonal, ModelWithCorners.convex_range', CFC.spectrum_abs, Submodule.starProjection_top, Submodule.iInf_orthogonal, ofReal_nnratCast, NormedSpace.sInter_polar_eq_closedBall, Affine.Simplex.orthogonalProjection_eq_circumcenter_of_dist_eq, lp.hasSum_inner, isBoundedBilinearMap_inner, TensorProduct.nnnorm_assoc, ofReal_pos, IsSelfAdjoint.conj_starProjection, re_le_norm, OrthonormalBasis.norm_le_card_mul_iSup_norm_inner, wInner_zero_left, Polynomial.aeval_ofReal, ContinuousLinearMap.orthogonal_range, Submodule.lipschitzWith_starProjection, ContinuousLinearMap.isPositive_iff_complex, instSymmEqInnerOfNat, ordinaryHypergeometricSeries_eq_zero_iff, InnerProductSpace.span_gramSchmidt, Orthonormal.inner_finsupp_eq_zero, ContinuousLinearMap.spectralRadius_eq_nnnorm, EuclideanGeometry.hasFDerivAt_inversion, ofNat_im, torusIntegral_smul, range_cfcHom_le, Continuous.cfcβ', LinearMap.coe_isometryOfOrthonormal, OrthonormalBasis.span_apply, inner_sub_right, ClosedSubmodule.orthogonal_toSubmodule_eq, EuclideanGeometry.vsub_orthogonalProjection_mem_direction, ContinuousLinearMap.isStarProjection_iff_isIdempotentElem_and_isStarNormal, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, spectrum.exp_mem_exp, ContinuousLinearMap.isPositive_iff, TensorProduct.mapIsometry_apply, InnerProductSpace.Core.inner_add_right, MeasureTheory.charFun_map_mul_comp, Matrix.IsHermitian.cfcAux_id, ContinuousOn.cfc', cfcβAux_mem_range_inr, inv_pos, ContinuousMap.adjoin_id_eq_span_one_add, IsSelfAdjoint.hasEigenvector_of_isMinOn, LinearMap.IsSymmetric.sub, ProbabilityTheory.covarianceBilin_map, IsHilbertSum.linearIsometryEquiv_symm_apply_dfinsupp_sum_single, real_smul_ofReal, cfcβ_norm_sq_nonneg, SchwartzMap.instFourierSMul, SchwartzMap.fourierTransformCLM_apply, HasFDerivAt.curveIntegral_segment_source', AffineSubspace.signedInfDist_singleton, norm_sq_eq_def, Affine.Simplex.coe_orthogonalProjection_vadd_smul_vsub_orthogonalProjection, Matrix.IsHermitian.coe_re_diag, LinearIsometryEquiv.smul_trans, SchwartzMap.fderivCLM_fourier_eq, MeasureTheory.L2.mem_L1_inner, SchwartzMap.derivCLM_apply, TensorProduct.toLinearMap_mapIsometry, map_nonneg_iff, ratCast_im, LinearMap.singularValues_finrank_range_self, Unitary.inner_map_map, I_mul_re, TensorProduct.enorm_map, uniformEquicontinuous_birkhoffAverage, LinearMap.IsSymmetric.det_eq_prod_eigenvalues, wInner_neg_left, LinearMap.IsSymmetric.id, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, inner_gradientWithin_left, conj_eq_iff_im, ContinuousLinearMap.adjoint_comp, HasCompactSupport.hasDerivAt_convolution_left, WithLp.volume_preserving_ofLp, SchwartzMap.integral_clm_comp_deriv_right_eq_neg_left, Commute.cfcβ, curveIntegralFun_restrictScalars, EuclideanGeometry.Sphere.IsTangent.isTangentAt, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.adjointAux_inner_right, HilbertBasis.repr_self, conj_re_ax, TensorProduct.commIsometry_apply, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular', Module.Basis.coe_toOrthonormalBasis, MeasureTheory.condExpInd_smul', InnerProductSpace.Core.inner_self_of_eq_zero, ContinuousAt.cfcβ, mul_self_norm, TensorProduct.congrIsometry_symm, LinearMap.isStarProjection_toContinuousLinearMap_iff, ContinuousLinearMap.IsPositive.orthogonalProjection_comp, Matrix.IsHermitian.roots_charpoly_eq_eigenvaluesβ, LinearMap.IsSymmetric.orthogonal_range, MeasureTheory.L2.integrable_inner, LinearPMap.adjointDomainMkCLMExtend_apply, nnnorm_cfcβ_le_iff, dimH_orthogonalProjection_le, MeasureTheory.charFun_map_mul, inner_mul_symm_re_eq_norm, EuclideanGeometry.Sphere.mem_inter_orthRadius_iff_vsub_mem_and_norm_sq, curveIntegral_fun_sub, Submodule.re_inner_starProjection_nonneg, ContDiffWithinAt.inner, Submodule.adjoint_orthogonalProjection, MeasureTheory.MemLp.im, EuclideanGeometry.reflection_apply', OrthogonalFamily.sum_projection_of_mem_iSup, hasFDerivWithinAt_iff_hasGradientWithinAt, CurveIntegrable.smul, LinearMap.IsSymmetric.trace_eq_sum_eigenvalues, Submodule.id_eq_sum_starProjection_self_orthogonalComplement, Submodule.isOrtho_bot_right, LinearMap.adjoint_comp, EuclideanGeometry.oangle_self_orthogonalProjection, StrongDual.extendRCLike_apply, norm_coe_norm, LinearMap.IsPositive.inner_nonneg_right, Matrix.toEuclideanLin_apply_piLp_toLp, realRingEquiv_apply, InnerProductSpace.inner_gramSchmidtOrthonormalBasis_eq_zero, InnerProductSpace.span_gramSchmidt_Iio, hasFDerivAt_integral_of_dominated_of_fderiv_le, LinearIsometryEquiv.lTensor_def, mul_im, ContDiff.hasStrictDerivAt, Submodule.starProjection_orthogonal_apply_eq_zero, nnnorm_cfc_lt_iff, IsContDiffImplicitAt.contDiffAt_implicitFunction, Submodule.mem_orthogonal_singleton_iff_inner_left, ofReal_tsum, Submodule.mem_adjoint_iff, normSq_div, im_sq_le_normSq, LinearMap.isSymmetric_iff_isSelfAdjoint, inner_eq_zero_symm, lipschitzWith_ofReal, integrableOn_mul_sum_Icc, EuclideanSpace.dist_eq, Submodule.reflection_involutive, SchwartzMap.convolution_flip, Orthonormal.orthogonalFamily, LinearMap.isSymmetric_iff_sesqForm, hasStrictDerivAt_exp, ContinuousLinearMap.IsPositive.adjoint_conj, LinearIsometryEquiv.reflections_generate_dim, Convex.exists_forall_hasFDerivWithinAt_of_hasFDerivWithinAt_symmetric, Submodule.orthogonal_le, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection, LinearMap.bound_of_sphere_bound, ContinuousLinearMap.abs_rayleighQuotient_le_of_norm_mem_resolventSet, InnerProductSpace.gramSchmidtOrthonormalBasis_inv_triangular, RKHS.kernel_inner, LinearMap.isSymmetricProjection_iff_eq_coe_starProjection_range, intervalIntegral.integral_smul_const, MeasureTheory.hausdorffMeasure_orthogonalProjection_le, HilbertBasis.summable_inner_mul_inner, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces_invariant, ContinuousLinearMap.isPositive_iff', Submodule.finrank_add_finrank_orthogonal, ContinuousLinearMap.star_eq_adjoint, Submodule.orthogonal_eq_top_iff, Submodule.lipschitzWith_orthogonalProjection, Affine.Simplex.abs_signedInfDist_eq_dist_of_mem_affineSpan_range, continuousOn_cfcβ_setProd, ProbabilityTheory.tendsto_charFun_inv_sqrt_mul_pow, volume_euclideanSpace_eq_dirac, LinearMap.IsSymmetric.orthogonalComplement_iSup_eigenspaces, LinearMap.isSymmetric_adjoint_comp_self, wInner_one_const_left, lipschitzWith_of_nnnorm_deriv_le, ProperCone.hyperplane_separation_of_notMem, OrthonormalBasis.inner_eq_one, ofReal_mul_neg_iff, Module.End.mem_invtSubmodule_adjoint_iff, orthogonalFamily_iff_pairwise, re_ofReal_pow, LDL.diag_eq_lowerInv_conj, re_inner_self_nonpos, norm_sq_re_add_conj, LinearMap.IsSymmetric.im_inner_apply_self, Submodule.inf_orthogonal_eq_bot, Matrix.IsHermitian.eigenvalues_mem_spectrum_real, Submodule.isOrtho_sSup_left, LinearMap.range_self_comp_adjoint, innerββ_apply, deriv_inner_apply, im_to_complex, Affine.Simplex.orthogonalProjectionSpan_reindex, innerSL_apply, OrthonormalBasis.coe_toBasis_repr, riesz_lemma_of_lt_one, InnerProductSpace.Core.cauchy_schwarz_aux', ContinuousLinearMap.tendsto_birkhoffAverage_orthogonalProjection, InnerProductSpace.isIdempotentElem_rankOne_self_iff, Submodule.norm_starProjection_apply, IsSelfAdjoint.hasEigenvector_of_isLocalExtrOn, stereographic_apply, MeasureTheory.inner_condExpL2_eq_inner_fun, StrongDual.toLp_apply, OrthogonalFamily.norm_sum, HasGradientAtFilter.tendsto_nhds, Submodule.inner_starProjection_left_eq_right, MeasureTheory.mem_lpMeas_self, ContinuousLinearMap.IsPositive.spectrumRestricts, OrthonormalBasis.sum_repr, re_eq_complex_re, TemperedDistribution.derivCLM_toTemperedDistributionCLM_eq, Submodule.reflection_mem_subspace_eq_self, Orthonormal.mapLinearIsometryEquiv, MeasureTheory.integrableOn_condExpL2_of_measure_ne_top, IsCoercive.ker_eq_bot, InnerProductSpaceable.innerProp, OrthogonalFamily.independent, norm_to_complex, Submodule.fstL_comp_coe_orthogonalDecomposition, inner_smul_left_eq_smul, imCLM_coe, re_sq_le_normSq, isStarProjection_iff_eq_starProjection_range, ContinuousLinearMap.reApplyInnerSelf_smul, conj_inv, LinearIsometryEquiv.symm_units_smul, LinearMap.IsSymmetric.roots_charpoly_eq_eigenvalues, IsHilbertSum.linearIsometryEquiv_symm_apply_single, IsSelfAdjoint.adjoint_conj, UnitAddTorus.mFourierBasis_repr, ContinuousLinearMap.eq_zero_of_forall_hasEigenvalue_eq_zero, HasDerivAt.inner, LinearIsometryEquiv.toLinearIsometry_rTensor, Submodule.starProjection_minimal, EuclideanGeometry.orthogonalProjection_linear, OrthonormalBasis.sum_rankOne_eq_id, norm_apply_le_norm_cfc, fourierBasis_repr, Submodule.orthogonalProjection_orthogonal_apply_eq_zero, AffineSubspace.signedInfDist_def, Submodule.starProjection_mem_subspace_eq_self, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, InnerProductSpace.gramSchmidt_linearIndependent, MeasureTheory.taylorWithinEval_charFun_two_zero', AnalyticOn.hasFPowerSeriesOnBall, MeasureTheory.integral_fintype_prod_volume_eq_prod, mul_re, TensorProduct.norm_tmul, LinearMap.isPositive_iff, integrable_cfc, LinearIsometryEquiv.symm_smul_apply, SchwartzMap.tsupport_derivCLM_subset, Affine.Simplex.orthogonalProjectionSpan_eulerPoint_mem_ninePointCircle, normSq_zero, OrthonormalBasis.coe_toBasis_repr_apply, enorm_conj, inner_smul_right_eq_smul, LinearIsometryEquiv.star_eq_symm, orthonormal_iff_ite, wInner_add_left, SchwartzMap.integral_smul_laplacian_right_eq_left, EuclideanGeometry.reflection_involutive, ContinuousOn.inner, re_le_neg_norm_iff_eq_neg_norm, OrthonormalBasis.coe_equiv_euclideanSpace, StrongDual.im_extendRCLike_apply, conjAe_coe, continuous_cfcβAux, neg_iff_exists_ofReal, wInner_one_eq_sum, InnerProductSpace.Core.inner_add_add_self, inner_self_eq_one_of_norm_one, norm_cfcHom, toContinuousLinearMap_complexLinearIsometryEquiv, to_complex_nonneg_iff, EuclideanSpace.dist_sq_eq, integral_ofReal, sqrt_zero, Submodule.orthogonalProjectionFn_eq, TensorProduct.nnnorm_comm, Submodule.IsOrtho.ge, Affine.Simplex.signedInfDist_affineCombination, tendsto_sum_mul_atTop_nhds_one_sub_integral, Submodule.bot_orthogonal_eq_top, signedDist_apply, UniformSpace.Completion.inner_coe, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, ContinuousLinearMap.IsPositive.conj_starProjection, ProbabilityTheory.iIndepFun.integral_fun_prod_eq_prod_integral, EuclideanGeometry.angle_self_orthogonalProjection, LinearMap.IsSymmetric.charpoly_eq, EuclideanSpace.inner_toLp_toLp, Orthonormal.comp_linearIsometryEquiv, im_ofReal_mul, Submodule.map_orthogonal, Matrix.l2_opNNNorm_diagonal, inner_self_re_eq_norm, HasFDerivAt.hasGradientAt, ordinaryHypergeometric_radius_top_of_neg_natβ, Matrix.instCStarRing, normSq_eq_zero, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, AffineSubspace.direction_perpBisector, instOrderClosedTopology, LinearIsometryEquiv.toMatrix_mem_unitaryGroup, LinearMap.IsSymmetric.conj_inner_sym, Filter.Tendsto.inner, geometric_hahn_banach_of_nonempty_interior, LinearMap.IsSymmetric.LinearMap.IsSymmetric.directSum_isInternal_of_pairwise_commute, MeasureTheory.Integrable.const_inner, OrthonormalBasis.same_orientation_iff_det_eq_det, ContinuousLinearMap.extendToπ'_apply, ClosedSubmodule.orthogonal_disjoint, I_re, ContinuousLinearMap.isAdjointPair_inner, TensorProduct.norm_map, dist_birkhoffAverage_birkhoffAverage_le, ContinuousLinearMap.coe_le_coe_iff, AddChar.linearIndependent, instPosMulReflectLE, SchwartzMap.fourierMultiplierCLM_fourierMultiplierCLM_apply, EuclideanGeometry.orthogonalProjection_eq_self_iff, ContinuousLinearMap.IsIdempotentElem.isSelfAdjoint_iff_isStarNormal, re_extendToπβ, im_eq_complex_im, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, EuclideanGeometry.reflection_subtype, Submodule.orthogonal_le_orthogonal_iff, Submodule.orthogonal_le_iff_orthogonal_le, Orientation.finOrthonormalBasis_orientation, ofReal_im_ax, ContinuousLinearEquiv.coord_norm', cfc_setIntegral', ContinuousLinearMap.IsStarProjection.isSymmetricProjection, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, ContinuousLinearMap.isPositive_zero, cfcβ_setIntegral', LinearMap.support_singularValues, Submodule.snd_orthogonalDecomposition_apply, cfcβ_apply_mem_elemental, InnerProductSpace.Core.inner_self_im, Matrix.IsHermitian.eigenvalues_eq_zero_iff, SchwartzMap.fourier_fderivCLM_eq, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, ContinuousLinearMap.integral_comp_id_comm, hasStrictFDerivAt_exp_smul_const, StrongDual.re_extendRCLike_apply, SchwartzMap.fourier_convolution_apply, instNormSMulClassInt, Submodule.starProjection_le_starProjection_iff, ContDiffAt.inner, wInner_cWeight_const_right, inv_eq_conj, sum_mul_eq_sub_sub_integral_mul', gauge_smul, ContinuousMap.elemental_id_eq_top, ProbabilityTheory.multivariateGaussian_zero_one, LinearMap.eq_adjoint_iff_basis_right, Submodule.instOrthogonalCompleteSpace, IsSelfAdjoint.commute_cfcβ, AEMeasurable.re, hasDerivAt_exp_smul_const', instOrderIsoClassContinuousLinearMapIdOfNonUnitalAlgEquivClassOfStarHomClassOfContinuousMapClass, LinearMap.isStarProjection_iff_isSymmetricProjection, LinearIsometryEquiv.toLinearEquiv_rTensor, EuclideanSpace.nnnorm_eq, norm_apply_le_norm_cfcβ, innerββ_apply_coe, nnnorm_natCast, PiLp.inner_apply, ContDiffAt.to_localInverse, LinearMap.orthogonal_range, Submodule.orthogonalDecomposition_apply, Submodule.isOrtho_self, LinearIsometryEquiv.toLinearIsometry_lTensor, AddChar.wInner_cWeight_eq_boole, IsContDiffImplicitAt.implicitFunction_def, LinearMap.singularValues_of_lt, EuclideanSpace.restrictβ_apply, NumberField.mixedEmbedding.euclidean.volumePreserving_toMixed_symm, ProbabilityTheory.iIndepFun.integral_fun_prod_comp, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, range_cfcHom, iInter_halfSpaces_eq', re_ofReal_mul, norm_add_pow_two, ClosedSubmodule.orthogonal_closure, AddChar.map_neg_eq_conj, hasGradientWithinAt_iff_tendsto, InnerProductSpace.add_left, OrthonormalBasis.toMatrix_orthonormalBasis_mem_orthogonal, EuclideanSpace.inner_single_right, sum_mul_eq_sub_integral_mul, norm_eq_sqrt_re_inner, iInter_halfSpaces_eq, Matrix.IsHermitian.rank_eq_card_non_zero_eigs, inner_self_nonneg, HasFDerivWithinAt.curveIntegral_segment_source', nnnorm_cfcHom, normSq_to_complex, integrableOn_cfc, OrthonormalBasis.orientation_adjustToOrientation, continuous_im, continuousOn_cfc, EuclideanGeometry.orthogonalProjection_vsub_mem_direction_orthogonal, LinearMap.IsSymmetric.re_trace_eq_sum_eigenvalues, MeasureTheory.lpMeasToLpTrim_ae_eq, Submodule.orthogonal_eq_inter, Convex.hasFDerivWithinAt_curveIntegral_segment_of_hasFDerivWithinAt_symmetric, normSq_add, MeasureTheory.eLpNorm_condExpL2_le, div_re, ProbabilityTheory.iIndepFun.integral_prod_comp, setIntegral_re_add_im, geometric_hahn_banach_compact_closed, SchwartzMap.smulLeftCLM_ofReal, LinearMap.IsPositive.adjoint_eq, fderiv_norm_rpow, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, Matrix.toEuclideanLin_eq_toLin_orthonormal, LinearMap.isometryOfOrthonormal_toLinearMap, MeasureTheory.lpMeasToLpTrim_smul, Submodule.starProjection_orthogonal_val, isStarProjection_iff_eq_starProjection, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, geometric_hahn_banach_point_closed, LinearMap.IsSymmetricProjection.le_iff_range_le_range, intervalIntegral_ofReal, UniformSpace.Completion.continuous_inner, EuclideanGeometry.eq_orthogonalProjection_of_eq_subspace, EuclideanGeometry.orthogonalProjection_apply, IsometricContinuousFunctionalCalculus.isGreatest_norm_spectrum, curveIntegral_def', re_inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four, EuclideanGeometry.Sphere.direction_orthRadius, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, EuclideanGeometry.eq_reflection_of_eq_subspace, OrthonormalBasis.coe_singleton, LinearIsometry.rTensor_apply, NormedSpace.polar_closedBall, Submodule.norm_orthogonalProjection, ClosedSubmodule.symplComp_sup, Matrix.l2_opNNNorm_conjTranspose_mul_self, Submodule.instHasOrthogonalProjectionTop, AffineSubspace.signedInfDist_apply_self, EuclideanGeometry.orthogonalProjection_vsub_orthogonalProjection, IsOpen.isOpen_inter_preimage_of_deriv_eq_zero, LinearIsometry.toLinearMap_lTensor, EuclideanGeometry.orthogonalProjection_mem_orthogonal, coe_innerββ_apply, ContinuousWithinAt.inner, IsSelfAdjoint.eq_smul_self_of_isLocalExtrOn, curveIntegral_add, EuclideanSpace.euclideanHausdorffMeasure_eq_volume, HasGradientAt.hasDerivAt, TensorProduct.nndist_tmul_le, hasDerivAt_exp_zero, MeasureTheory.charFun_map_eq_charFunDual_smul, InnerProductSpace.continuousLinearMapOfBilin_apply, hasGradientWithinAt_iff_isLittleO, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, norm_sub_pow_two, conj_eq_re_sub_im, DFinsupp.inner_sum, InnerProductSpace.Core.re_inner_smul_ofReal_smul_self, Submodule.HasOrthogonalProjection.map_linearIsometryEquiv, inner_matrix_row_row, MeasureTheory.condExpIndSMul_ae_eq_smul, ContinuousLinearMap.rayleighQuotient_neg_apply, MeasureTheory.intervalIntegrable_charFun, ContinuousMap.idealOf_compl_singleton_isMaximal, gaugeSeminorm_lt_one_of_isOpen, MeasureTheory.lpMeas.ae_fin_strongly_measurable', gaugeSeminormFamily_ball, curveIntegral_sub, cfcβL_integrable, sqrt_normSq_eq_norm, Matrix.IsHermitian.charpoly_eq, conj_ofNat, intervalIntegral.hasDerivAt_integral_of_dominated_loc_of_lip, HasGradientAt.fderiv_apply, SchwartzMap.instFourierInvSMul, TemperedDistribution.derivCLM_apply_apply, OrthonormalBasis.tensorProduct_apply, EuclideanGeometry.two_zsmul_oangle_orthogonalProjection_self, integral_re, ContinuousLinearMap.finite_dimensional_eigenspace, tendsto_ofReal_atBot_cobounded, HasCompactSupport.contDiff_convolution_right, LinearPMap.mem_adjoint_domain_of_exists, Complex.isometryOfOrthonormal_symm_apply, Matrix.instStarOrderedRing, normSq_apply, LinearMap.self_comp_adjoint_injective_iff, CurveIntegrable.sub, PreInnerProductSpace.Core.add_left, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, ofRealCLM_coe, intervalIntegral.integral_unitInterval_deriv_eq_sub, inner_gradient_left, TensorProduct.congrIsometry_apply, Submodule.starProjection_comp_starProjection_of_le, ConvexOn.exists_affine_le_of_lt, OrthonormalBasis.det_to_matrix_orthonormalBasis_real, MeasureTheory.integral_prod_smul, inner_sub_sub_self, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, innerSL_apply_coe, ContinuousLinearMap.isPositive_one, ContinuousLinearMap.isPositive_sum, instIsRCLikeNormedField, ordinaryHypergeometricSeries_norm_div_succ_norm, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, HasStrictFDerivAt.inner, ContinuousWithinAt.cfc, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, re_inner_le_norm, LinearMap.IsSymmetric.iSup_eigenspace_inf_eigenspace_of_commute, Submodule.orthogonalProjection_comp_subtypeL_eq_zero_iff, EuclideanGeometry.orthogonalProjection_sup_of_orthogonalProjection_eq, LinearMap.toMatrix_adjoint, Affine.Simplex.reflection_circumcenter_eq_affineCombination_of_pointsWithCircumcenter, Matrix.IsStrictlyPositive.posDef, inner_eq_one_iff_of_norm_one, ProbabilityTheory.charFun_gaussianReal, CFC.abs_smul, conj_smul, HilbertBasis.tsum_inner_mul_inner, EuclideanGeometry.coe_orthogonalProjection_eq_iff_mem, mul_re_ax, sum_mul_eq_sub_integral_mulβ, ContinuousLinearMap.isPositive_adjoint_comp_self, SchwartzMap.integral_clm_comp_laplacian_right_eq_left, ContinuousLinearMap.integral_comp_comm, EuclideanSpace.single_eq_zero_iff, TensorProduct.nnnorm_lid, LinearMap.im_inner_adjoint_mul_self_eq_zero, instTietzeExtension, Matrix.IsHermitian.mulVec_eigenvectorBasis, ClosedSubmodule.orthogonal_closure', Matrix.l2_opNorm_def, OrthogonalFamily.linearIsometry_apply, wInner_nonneg, Matrix.toEuclideanLin_toLp, nnnorm_cfcβ_le, OrthogonalFamily.pairwise, LinearMap.IsSymmetric.toMatrix_eigenvectorBasis, integral_re_add_im, continuous_stereoInvFun, Submodule.orthogonalProjection_eq_zero_iff, MeasureTheory.condExpL1CLM_smul, Matrix.l2_opNorm_mul, Subalgebra.SeparatesPoints.rclike_to_real, norm_innerSL_le, norm_inner_symm, OrthonormalBasis.measurePreserving_measurableEquiv, LinearEquiv.image_closure_of_convex', ContinuousLinearMap.IsPositive.isSelfAdjoint, Submodule.orthogonalProjection_starProjection_of_le, OrthonormalBasis.sum_repr', norm_le_im_iff_eq_I_mul_norm, real_smul_eq_coe_mul, Submodule.coe_orthogonalProjection_apply, Submodule.starProjection_coe_eq_isCompl_projection, ofReal_inv, ContinuousMap.idealOfSet_ofIdeal_isClosed, ofRealAm_coe, normSq_one, re_to_complex, orthonormal_vecCons_iff, ContinuousLinearMap.IsIdempotentElem.hasOrthogonalProjection_range, SchwartzMap.integral_smul_deriv_right_eq_neg_left, LinearMap.posSemidef_toMatrix_iff, Submodule.starProjection_apply_eq_zero_iff, SchwartzMap.fourier_convolution, hasSum_im, ContinuousLinearMap.orthogonal_mem_invtSubmodule, Orthonormal.inner_right_fintype, charZero_rclike, EuclideanSpace.nndist_single_same, OrthonormalBasis.abs_det_adjustToOrientation, HasGradientWithinAt.hasFDerivWithinAt, EuclideanSpace.edist_eq, hasFDerivAt_exp, EuclideanSpace.single_apply, isCauSeq_re, Pi.orthonormalBasis_repr, hasSum_conj', Matrix.PosDef.det_pos, IsHilbertSum.linearIsometryEquiv_apply_dfinsupp_sum_single, InnerProductSpace.conj_inner_symm, I_im', Orthonormal.tmul, Submodule.IsCompl.projection_isSymmetric_iff, MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero, LinearMap.isAdjointPair_inner, MeasureTheory.condExpIndL1Fin_smul', LinearMap.IsPositive.adjoint_conj, LinearMap.tendsto_birkhoffAverage_of_ker_subset_closure, LinearMap.isPositive_one, ClosedSubmodule.symplComp_inf, re_eq_self_of_le, Affine.Triangle.dist_orthocenter_reflection_circumcenter_finset, Affine.Simplex.affineSpan_pair_eq_altitude_iff, RKHS.posSemidef_kernel, range_cfc, sum_mul_eq_sub_sub_integral_mul, wInner_add_right, Affine.Simplex.direction_altitude, LinearIsometryEquiv.symm_lTensor, DifferentiableWithinAt.inner, Submodule.isOrtho_bot_left, MeasureTheory.contDiffOn_convolution_right_with_param_aux, Submodule.exists_norm_eq_iInf_of_complete_subspace, EuclideanGeometry.dist_orthogonalProjection_line_eq_iff_two_zsmul_oangle_eq, LinearPMap.adjointAux_inner, HilbertBasis.hasSum_inner_mul_inner, LinearIsometryEquiv.toContinuousLinearEquiv_smul, fderivInnerCLM_apply, Orthonormal.sum_inner_products_le, EuclideanGeometry.orthogonalProjection_eq_iff_mem, ConvexOn.sSup_affine_eq, EuclideanGeometry.dist_orthogonalProjection_line_eq_of_two_zsmul_oangle_eq, Submodule.orthogonalProjection_coe_eq_linearProjOfIsCompl, LinearMap.IsSymmetric.hasEigenvector_eigenvectorBasis, I_mul_I_of_nonzero, I_mul_I_ax, SchwartzMap.toZeroAtInftyCLM_apply, summable_mul_of_bigO_atTop', LinearMap.IsSymmetric.coe_re_inner_apply_self, span_one_I, OrthogonalFamily.summable_iff_norm_sq_summable, HasGradientAtFilter.hasDerivAtFilter, CurveIntegrable.add, Convex.lipschitzOnWith_of_nnnorm_deriv_le, geometric_hahn_banach_closed_compact, MeasureTheory.eLpNorm_conj, inner_gradient_right, MeasureTheory.lpMeasToLpTrimLie_symm_toLp, LinearIsometryEquiv.conjStarAlgEquiv_apply_apply, DFinsupp.sum_inner, Real.fourierIntegral_iteratedFDeriv, hasStrictDerivAt_exp_zero, Orthonormal.equiv_apply, Submodule.orthogonalProjection_norm_le, Matrix.PosDef.posDef_sqrt, norm_cfcβ_le_iff, LinearMap.ker_le_ker_of_range, EuclideanSpace.volume_closedBall, intCast_im, ofReal_sum, ContinuousMap.idealOfSet_ofIdeal_eq_closure, SchwartzMap.fourierMultiplierCLM_smul, finrank_euclideanSpace_fin, Submodule.orthogonalProjection_orthogonal, inner_conj_symm, norm_of_nonneg', LinearIsometryEquiv.rTensor_def, MeasureTheory.norm_condExpL2_le_one, AddChar.inv_apply_eq_conj, OrthonormalBasis.repr_reindex, MeasureTheory.condExpL2_comp_continuousLinearMap, inner_im_symm, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, Submodule.orthogonalProjection_orthogonalComplement_singleton_eq_zero, Submodule.isOrtho_sup_left, MeasureTheory.memLp_re_im_iff, ContinuousLinearMap.adjoint_innerSL_apply, EuclideanGeometry.reflection_mem_of_le_of_mem, gaugeSeminorm_toFun, Submodule.IsOrtho.comap, OrthogonalFamily.inner_right_fintype, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, EuclideanGeometry.Sphere.dist_orthogonalProjection_eq_radius_iff_isTangentAt, binomialSeries_radius_ge_one, normSq_sub, InnerProductSpace.Core.toSeminormedSpaceCore, Submodule.orthogonalProjection_eq_linearProjOfIsCompl, Orthonormal.inner_sum, EuclideanGeometry.reflection_apply, intervalIntegral.integral_mul_const, LinearPMap.adjoint_apply_of_dense, hasStrictDerivAt_of_hasDerivAt_of_continuousAt, re_tsum, ContinuousLinearMap.IsPositive.re_inner_nonneg_right, wInner_cWeight_eq_smul_wInner_one, ContinuousMap.idealOfSet_isMaximal_iff, ContinuousLinearMap.integral_id_map, sqrt_neg_of_nonneg, MeasureTheory.condExpL2_const_inner, ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero, curveIntegrable_restrictScalars_iff, ContDiffAt.hasStrictDerivAt', LinearMap.IsSymmetric.intCast, IsCoercive.isClosed_range, realLinearIsometryEquiv_apply, InnerProductSpace.Core.inner_zero_left, TensorProduct.ext_iff_inner_right_threefold, curveIntegralFun_def, Matrix.tracePositiveLinearMap_apply, InnerProductSpaceable.inner_.conj_symm, ContinuousLinearMap.intervalIntegral_comp_comm, inner_eq_ofReal_norm_sq_right_iff, tendsto_ofReal_atTop_cobounded, CurveIntegrable.neg, EuclideanGeometry.dist_set_eq_iff_dist_orthogonalProjection_eq, Matrix.IsHermitian.instContinuousFunctionalCalculus, MeasureTheory.integral_convolution, contDiff_euclidean, fderiv_norm_sq_apply, Submodule.starProjection_eq_self_iff, IsSelfAdjoint.commute_cfc, imCLM_apply, cfcHom_apply_mem_elemental, LinearMap.IsSymmetric.sort_roots_charpoly_eq_eigenvalues, OrthonormalBasis.tensorProduct_repr_tmul_apply, conj_neg_I, ConvexOn.univ_sSup_of_nat_affine_eq, cfc_setIntegral, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, inv_I, TensorProduct.assocIsometry_symm_apply, Submodule.starProjection_tendsto_closure_iSup, NonUnitalIsometricContinuousFunctionalCalculus.nnnorm_quasispectrum_le, InnerProductSpace.Core.inner_conj_symm, InnerProductSpace.gramSchmidt_mem_span, MeasureTheory.Measure.euclideanHausdorffMeasure_def, MeasureTheory.MemLp.ofReal, Submodule.reflection_mem_subspace_orthogonalComplement_eq_neg, SchwartzMap.laplacian_eq_fourierMultiplierCLM, LinearMap.IsSymmetric.add, inner_eq_wInner_one, TensorProduct.inner_map_map, geometric_hahn_banach_open_open, MeasureTheory.integral_mul_const, lipschitzWith_im, fderiv_norm_sq, LinearMap.IsSymmetric.orthogonalFamily_iInf_eigenspaces, ContinuousMap.idealOpensGI_choice, LinearMap.IsPositive.toLinearMap_symm, TensorProduct.toLinearMap_mapInclIsometry, OrthogonalFamily.inner_right_dfinsupp, LinearPMap.adjoint_graph_eq_graph_adjoint, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', orthonormal_span, norm_cfc_lt, OrthogonalFamily.projection_directSum_coeAddHom, ContinuousLinearMap.innerSL_apply_comp, TensorProduct.lidIsometry_symm_apply, ContinuousLinearMap.instStarOrderedRingRCLike, surjective_stereographic, inner_vsub_left_eq_zero_symm, MeasureTheory.FiniteMeasure.tendsto_iff_forall_integral_rclike_tendsto, ContinuousLinearMap.toSesqForm_apply_norm_le, HilbertBasis.hasSum_repr_symm, inner_neg_left, hasFDerivAt_stereoInvFunAux_comp_coe, LinearMap.adjoint_id, inner_smul_left, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, integral_im, cfc_integral', MeasureTheory.condExpL2_indicator_nonneg, ContinuousLinearMap.adjoint_adjoint, HasCompactSupport.hasFDerivAt_convolution_left, restrict_toContinuousMap_eq_toContinuousMapStar_restrict, im_le_norm, ContinuousLinearMap.opNorm_le_of_re_inner_le, fderiv_inner_apply, norm_inner_le_norm, inner_matrix_col_col, DirectSum.IsInternal.subordinateOrthonormalBasisIndex_def, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, Affine.Simplex.altitude_def, div_I, normSq_conj, OrthonormalBasis.inner_eq_ite, ContinuousLinearMap.orthogonal_ker, ContinuousLinearMap.LinearMap.IsSymmetricProjection.isStarProjection, complexLinearIsometryEquiv_apply, InnerProductSpace.norm_rankOne, ProbabilityTheory.IndepFun.integral_mul_eq_mul_integral, cfc_mem, hasFDerivAt_integral_of_dominated_loc_of_lip, Convex.lipschitzOnWith_of_nnnorm_derivWithin_le, Submodule.isHilbertSumOrthogonal, inv_re, ofReal_ratCast, MeasureTheory.taylorWithinEval_charFun_zero, LinearMap.singularValues_eq_zero_iff_le_finrank_range, real_inner_I_smul_self, LinearIsometry.lTensor_def, Matrix.PosDef.re_dotProduct_pos, Orthonormal.inner_right_sum, ContinuousLinearMap.antilipschitz_of_forall_le_inner_map, TensorProduct.edist_tmul_le, unitary.inner_map_map, LinearMap.IsPositive.conj_adjoint, norm_of_nonneg, Orthonormal.tsum_inner_products_le, Matrix.gram_single, LinearMap.IsSymmetric.pow, InnerProductSpace.Core.inner_sub_right, LinearMap.IsSymmetric.orthogonalComplement_mem_invtSubmodule, EuclideanGeometry.orthogonalProjection_mem_subspace_eq_self, curveIntegralFun_zero, MeasureTheory.Integrable.im, LinearMap.IsSymmetric.eigenvalues_eq_eigenvalues_iff, Submodule.orthogonalProjectionFn_mem, Orthonormal.inner_eq_zero, LinearMap.IsPositive.re_inner_nonneg_left, zero_im, ContinuousLinearMapWOT.ext_inner_iff, cfcβ_integral', Matrix.permMatrix_l2_opNorm_eq, im_eq_zero, norm_inner_div_norm_mul_norm_eq_one_iff, MeasureTheory.lpMeas.aestronglyMeasurable, geometric_hahn_banach_open_point, Affine.Triangle.dist_orthogonalProjectionSpan_faceOpposite_eq_iff_two_zsmul_oangle_eq, Submodule.mem_iff_norm_starProjection, LinearMap.IsSymmetric.eigenvectorBasis_def, IsCoercive.antilipschitz, LinearMap.card_support_singularValues, InnerProductSpace.gramSchmidt_inv_triangular, LinearMap.IsSymmetric.apply_clm, Orthonormal.comp_linearIsometry, hasStrictFDerivAt_euclidean, unitary.linearIsometryEquiv_coe_apply, HilbertBasis.finite_spans_dense, nnnorm_cfcβ_lt, LinearMap.IsSymmetric.mul_of_commute, ofReal_lt_zero, LinearIsometry.adjoint_comp_self
|
toStarRing π | CompOp | 533 mathmath: Matrix.l2_opNorm_toEuclideanCLM, Pi.comul_eq_adjoint, LinearMap.IsSymmetric.clm_adjoint_eq, conj_re, integrableOn_cfcβ', MeasureTheory.lpNorm_conj, continuous_cfcβHomSuperset_left, LinearMap.IsSymmetric.conj_eigenvalue_eq_self, cfcβL_integral, ContinuousLinearMap.isPositive_iff_eq_sum_rankOne, continuousOn_stereoToFun, InnerProductSpace.isPositive_rankOne_self, Orthonormal.inner_left_finsupp, norm_cfcβHom, LinearMap.adjoint_adjoint, Matrix.IsHermitian.isClosedEmbedding_cfcAux, InnerProductSpace.toLinearIsometry_toDual, IsSelfAdjoint.commute_cfcHom, cfcβ_norm_nonneg, ContinuousWithinAt.cfcβ, hasFDerivAt_iff_hasGradientAt, cfcβHom_apply_mem_elemental, Filter.Tendsto.cfc, InnerProductSpace.rankOne_one_left_eq_innerSL, cfc_mem_elemental, nnnorm_cfc_lt, Matrix.IsHermitian.det_abs, LinearMap.isPositive_adjoint_comp_self, InnerProductSpace.isIdempotentElem_rankOne_self, Matrix.cstar_nnnorm_def, Matrix.IsHermitian.cfc_eq, star_def, integrableOn_cfc', inner_apply', LinearMap.orthogonal_ker, flip_innerSL_real, Matrix.le_iff, norm_cfc_lt_iff, sub_conj, isClosedEmbedding_cfcβAux, innerSL_apply_apply, CFC.abs_eq_cfcβ_coe_norm, LinearMap.adjoint_innerββ_apply, EuclideanSpace.inner_single_left, ContinuousLinearMap.innerSL_apply_comp_of_isSymmetric, LinearMap.adjoint_eq_toCLM_adjoint, nnnorm_cfcβ_lt_iff, ContinuousOn.cfcβ', OrthonormalBasis.orthogonalProjection_eq_sum_rankOne, InnerProductSpace.Core.inner_smul_left, InnerProductSpace.toDual_symm_apply, conj_nat_cast, IsGreatest.nnnorm_cfcβ, ContinuousAt.cfc, MeasureTheory.charFun_toDual_symm_eq_charFunDual, PreInnerProductSpace.Core.smul_left, Differentiable.fderiv_norm_rpow, toStarOrderedRing, is_real_TFAE, inner_gradientWithin_right, ContinuousLinearMap.adjoint_id, InnerProductSpace.smul_left, ContinuousLinearMap.isStarNormal_iff_norm_eq_adjoint, LinearMap.toMatrixOrthonormal_reindex, LinearMap.ker_self_comp_adjoint, Matrix.IsHermitian.eigenvalues_eq, norm_cfc_le_iff, mul_conj, norm_conj, Matrix.PosDef.eigenvalues_pos, InnerProductSpace.inner_left_rankOne_apply, cfcHom_mem_elemental, cfcβHom_mem_elemental, HasFDerivAt.norm_sq, polynomialFunctions.starClosure_topologicalClosure, innerββ_apply_apply, ContinuousLinearMap.eq_adjoint_iff, Continuous.cfc', InnerProductSpace.rankOne_apply, nonUnitalContinuousFunctionalCalculus, HasDerivAt.hasGradientAt, cfcβ_integral, IsSelfAdjoint.adjoint_eq, LinearMap.isHermitian_toMatrix_iff, RKHS.kernel_apply, TensorProduct.adjoint_map, cfcβ_setIntegral, LinearMap.ker_adjoint_comp_self, ContinuousLinearMap.isPositive_self_comp_adjoint, LinearMap.adjoint_toContinuousLinearMap, Matrix.IsHermitian.eigenvectorUnitary_col_eq, LDL.lowerInv_eq_gramSchmidtBasis, ContinuousLinearMap.toSesqForm_apply_coe, LinearIsometryEquiv.adjoint_eq_symm, LinearIsometryEquiv.trans_smul, im_eq_zero_iff_isSelfAdjoint, conjCLE_apply, Orthonormal.inner_left_fintype, LinearMap.IsSymmetric.conj_adjoint, cfcL_integrable, ContinuousLinearMap.adjointAux_norm, Pi.counit_eq_adjoint, LinearMap.toMatrixOrthonormal_apply_apply, instCStarRing, ContinuousOn.cfc, inrNonUnitalStarAlgHom_comp_cfcβHom_eq_cfcβAux, Real.fourier_iteratedFDeriv, LinearIsometryEquiv.adjoint_toLinearMap_eq_symm, nonUnitalContinuousFunctionalCalculusIsClosedEmbedding, InnerProductSpace.toDualMap_apply_apply, LinearMap.eq_adjoint_iff_basis_left, Matrix.PosSemidef.posDef_iff_isUnit, Matrix.IsHermitian.eigenvectorUnitary_mulVec, Module.Dual.norm_extendRCLike_apply_sq, coe_innerSL_apply, Matrix.PosSemidef.det_sqrt, range_cfcβHom, norm_cfcβ_lt, InnerProductSpace.nnnorm_rankOne, PreInnerProductSpace.Core.conj_inner_symm, range_cfc_subset, LinearMap.isSymmetric_self_comp_adjoint, InnerProductSpace.isSymmetricProjection_rankOne_self, Matrix.IsHermitian.charpoly_cfc_eq, IsGreatest.norm_cfcβ, hasGradientWithinAt_iff_hasFDerivWithinAt, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_left, Matrix.gram_eq_conjTranspose_mul, LinearIsometryEquiv.smul_apply, cfcβ_comp_norm, Continuous.cfcβ_of_mem_nhdsSet, cfcβHom_integral, Continuous.cfcβ, continuousOn_cfc_setProd, LinearMap.IsSymmetric.hasStrictFDerivAt_reApplyInnerSelf, conj_ofReal, Submodule.adjoint_subtypeL, IsGreatest.norm_cfc, LinearMap.isSymmetric_adjoint_mul_self, conjLIE_apply, conj_mul, Matrix.LE.le.posSemidef, InnerProductSpace.trace_rankOne, continuousOn_cfcβ, hasFDerivAt_norm_rpow, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, instContinuousMapUniqueHom, ContinuousLinearMap.IsPositive.conj_adjoint, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, contDiffOn_stereoToFun, Matrix.posDef_gram_of_linearIndependent, range_cfcβ, LinearMap.adjoint_rTensor, LinearMap.adjoint_inner_right, InnerProductSpace.adjoint_rankOne, InnerProductSpace.rankOne_eq_zero, IsGreatest.nnnorm_cfc, mul_wInner_left, re_eq_norm_of_mul_conj, InnerProductSpace.inner_right_rankOne_apply, HasFDerivWithinAt.hasGradientWithinAt, innerSL_inj, conj_eq_iff_re, cfcβAux_id, InnerProductSpace.rankOne_eq_rankOne_iff_comm, InnerProductSpace.toDual_apply, cfcβ_mem_elemental, conj_I_ax, InnerProductSpace.comp_rankOne, OrthonormalBasis.starProjection_eq_sum_rankOne, InnerProductSpace.toDualMap_apply, LinearMap.IsSymmetric.adjoint_conj, ContinuousLinearMap.adjoint_inner_left, InnerProductSpace.AlgebraOfCoalgebra.mul_def, cfcHom_integral, Matrix.l2_opNorm_conjTranspose_mul_self, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_right, Matrix.isSymmetric_toEuclideanLin_iff, nnnorm_apply_le_nnnorm_cfcβ, uniqueNonUnitalContinuousFunctionalCalculus, LinearMap.adjoint_comp_self_injective_iff, integral_conj, InnerProductSpace.rank_rankOne, IsometricContinuousFunctionalCalculus.toNonUnital, InnerProductSpace.toDual_apply_apply, Matrix.PosSemidef.eigenvalues_nonneg, ContinuousLinearMap.adjointAux_apply, ContinuousLinearMap.inner_map_map_iff_adjoint_comp_self, ProperCone.innerDual_singleton, add_conj, CFC.exp_eq_normedSpace_exp, im_eq_conj_sub, LDL.lower_conj_diag, Matrix.IsHermitian.posSemidef_iff_eigenvalues_nonneg, InnerProductSpace.rankOne_def, conj_im_ax, stereoToFun_apply, ContinuousLinearMap.adjointAux_inner_left, inner_self_conj, LinearIsometryEquiv.conjStarAlgEquiv_ext_iff, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, integrable_cfcβ, Matrix.l2_opNNNorm_conjTranspose, ClosedSubmodule.orthogonal_eq_inter, conj_div, HasDerivAtFilter.hasGradientAtFilter, Matrix.nonneg_iff_posSemidef, summable_conj, norm_cfcβ_lt_iff, Commute.cfcβHom, LinearMap.toMatrixOrthonormal_symm_apply, Matrix.posDef_gram_iff_linearIndependent, LinearMap.toMatrix_innerββ_apply, ContinuousLinearMap.IsStarNormal.adjoint_apply_eq_zero_iff, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, Matrix.inner_toEuclideanCLM, Matrix.PosSemidef.toLinearMapβ'_zero_iff, Matrix.l2_opNorm_conjTranspose, LinearMap.isSelfAdjoint_iff', innerSLFlip_apply_apply, InnerProductSpace.enorm_rankOne, Orthonormal.inner_finsupp_eq_sum_right, InnerProductSpace.continuousLinearMapOfBilin_zero, ContinuousLinearMap.toLinearMap_innerSL_apply, LinearMap.IsSymmetric.adjoint_eq, HasGradientAt.hasFDerivAt, Real.fourier_fderiv, ContinuousMap.adjoin_id_eq_span_one_union, HasFDerivWithinAt.norm_sq, Matrix.isHermitian_gram, LinearMap.IsSymmetric.isSymmetric_smul_iff, Matrix.isStrictlyPositive_iff_posDef, range_cfcβHom_le, Matrix.PosDef.commute_iff, Matrix.IsHermitian.cfcAux_apply, LinearMap.hasEigenvalue_adjoint_comp_self_sq_singularValues, Matrix.ofLp_toEuclideanCLM, Filter.Tendsto.cfcβ, ContinuousLinearMap.toPMap_adjoint_eq_adjoint_toPMap_of_dense, instContinuousStar, ProbabilityTheory.covarianceBilin_eq_covarianceBilinDual, inr_comp_cfcβHom_eq_cfcβAux, LinearMap.star_eq_adjoint, Matrix.isPositive_toEuclideanLin_iff, nnnorm_cfc_le_iff, Polynomial.aeval_conj, re_eq_add_conj, ContinuousLinearMap.isometry_iff_adjoint_comp_self, IsSelfAdjoint.conj_adjoint, wInner_const_left, wInner_cWeight_const_left, hasStrictFDerivAt_norm_sq, LinearMap.adjoint_toSpanSingleton, inner_apply, Matrix.posDef_iff_eq_conjTranspose_mul_self, LinearMap.re_inner_adjoint_mul_self_nonneg, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, LinearMap.isPositive_self_comp_adjoint, ContinuousLinearMap.ker_self_comp_adjoint, hasSum_conj, ContinuousLinearMap.instStarModuleId, continuous_cfcHomSuperset_left, LinearIsometry.adjoint_comp_self', Continuous.cfc_of_mem_nhdsSet, LinearIsometryEquiv.toLinearEquiv_smul, ContinuousLinearMap.adjointAux_adjointAux, LinearMap.eq_adjoint_iff, cfc_integral, LinearMap.norm_extendToπ'_apply_sq, ContinuousLinearMap.isSelfAdjoint_iff', conj_tsum, Matrix.PosSemidef.kronecker, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, wInner_const_right, InnerProductSpace.rankOne_def', Matrix.IsHermitian.eigenvectorUnitary_apply, ContinuousOn.cfc_of_mem_nhdsSet, ContinuousMapZero.mul_nonUnitalStarAlgHom_apply_eq_zero, ContinuousLinearMap.apply_norm_eq_sqrt_inner_adjoint_left, LinearMap.adjoint_lTensor, conj_eq_iff_real, LinearMap.toMatrixOrthonormal_apply, cfcβAux_injective, EuclideanSpace.inner_eq_star_dotProduct, Orthonormal.inner_left_sum, Orientation.inner_mul_areaForm_sub', Matrix.posSemidef_gram, LinearMap.singularValues_fin, LinearMap.sq_singularValues_of_lt, InnerProductSpace.innerSL_norm, cfcβ_mem, hasGradientAt_iff_hasFDerivAt, LinearMap.finrank_range_adjoint, LinearMap.sq_singularValues_fin, ContinuousLinearMap.adjoint_comp_self_injective_iff, Matrix.toLin_conjTranspose, instStarModuleReal, Orthonormal.inner_finsupp_eq_sum_left, LinearMap.range_adjoint_comp_self, Matrix.IsHermitian.spectral_theorem, integrableOn_cfcβ, norm_cfcβ_le, continuous_conj, InnerProductSpace.isStarProjection_rankOne_self, spec_cfcβAux, Matrix.IsHermitian.instContinuousFunctionalCalculusIsClosedEmbedding, integrable_cfcβ', ContinuousLinearMap.self_comp_adjoint_injective_iff, nnnorm_cfc_le, Matrix.IsHermitian.eigenvectorUnitary_coe, integrable_cfc', LinearMap.instStarModuleId, InnerProductSpace.rankOne_comp_rankOne, nnnorm_apply_le_nnnorm_cfc, Matrix.isHermitian_iff_isSymmetric, Continuous.cfc, Matrix.PosSemidef.inv_sqrt, Matrix.IsHermitian.cfcHom_eq_cfcAux, InnerProductSpace.rankOne_comp, Real.fourierIntegral_fderiv, InnerProductSpace.toMatrix_rankOne, conj_wInner_symm, InnerProductSpace.isSymmetric_rankOne_self, Commute.cfcHom, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, LinearMap.eq_adjoint_iff_basis, cfc_apply_mem_elemental, range_cfcβ_subset, Matrix.isSymmetric_toLin_iff, nnnorm_cfcβHom, ContinuousOn.cfcβ, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, ContinuousLinearMap.adjoint_toSpanSingleton, nnnorm_conj, cfc_comp_norm, wInner_one_const_right, Commute.cfc, Matrix.posSemidef_iff_eq_sum_vecMulVec, ContinuousLinearMap.ker_adjoint_comp_self, ContinuousOn.cfcβ_of_mem_nhdsSet, InnerProductSpace.rankOne_one_right_eq_toSpanSingleton, norm_sq_re_conj_add, innerSLFlip_apply, InnerProductSpace.toContinuousLinearMap_toDualMap, IsSelfAdjoint.commute_cfcβHom, conj_im, conj_I, cfcL_integral, innerSL_apply_norm, InnerProductSpace.toDual_apply_eq_toDualMap_apply, LinearMap.adjoint_inner_left, Matrix.star_dotProduct_gram_mulVec, inv_def, Matrix.PosDef.kronecker, innerSL_real_flip, MeasureTheory.charFun_eq_charFunDual_toDualMap, norm_cfc_le, toMatrix_innerSL_apply, Matrix.PosSemidef.re_dotProduct_nonneg, ContinuousLinearMap.orthogonal_range, range_cfcHom_le, Continuous.cfcβ', Matrix.PosSemidef.dotProduct_mulVec_zero_iff, Matrix.IsHermitian.cfcAux_id, ContinuousOn.cfc', cfcβAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, ProbabilityTheory.covarianceBilin_map, cfcβ_norm_sq_nonneg, LinearIsometryEquiv.smul_trans, OrthonormalBasis.toMatrix_orthonormalBasis_mem_unitary, conj_eq_iff_im, ContinuousLinearMap.adjoint_comp, Commute.cfcβ, InnerProductSpace.toLinearMap_rankOne, ContinuousLinearMap.adjointAux_inner_right, conj_re_ax, ContinuousAt.cfcβ, nnnorm_cfcβ_le_iff, Submodule.adjoint_orthogonalProjection, hasFDerivWithinAt_iff_hasGradientWithinAt, LinearMap.adjoint_comp, nnnorm_cfc_lt_iff, LinearMap.isSymmetric_iff_sesqForm, ContinuousLinearMap.IsPositive.adjoint_conj, ContinuousLinearMap.star_eq_adjoint, continuousOn_cfcβ_setProd, LinearMap.isSymmetric_adjoint_comp_self, wInner_one_const_left, ProperCone.hyperplane_separation_of_notMem, Module.End.mem_invtSubmodule_adjoint_iff, LDL.diag_eq_lowerInv_conj, norm_sq_re_add_conj, LinearMap.range_self_comp_adjoint, innerββ_apply, innerSL_apply, InnerProductSpace.isIdempotentElem_rankOne_self_iff, InnerProductSpaceable.innerProp, conj_inv, LinearIsometryEquiv.symm_units_smul, IsSelfAdjoint.adjoint_conj, OrthonormalBasis.sum_rankOne_eq_id, norm_apply_le_norm_cfc, MeasureTheory.BoundedContinuousFunction.inner_toLp, ContinuousLinearMap.adjoint_inner_right, integrable_cfc, LinearIsometryEquiv.symm_smul_apply, enorm_conj, conjAe_coe, continuous_cfcβAux, norm_cfcHom, signedDist_apply, Matrix.IsHermitian.star_mul_self_mul_eq_diagonal, EuclideanSpace.inner_toLp_toLp, HasFDerivAt.hasGradientAt, Matrix.instCStarRing, Matrix.IsHermitian.eigenvectorUnitary_transpose_apply, LinearIsometryEquiv.toMatrix_mem_unitaryGroup, LinearMap.IsSymmetric.conj_inner_sym, ContinuousLinearMap.isAdjointPair_inner, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, Matrix.IsHermitian.posDef_iff_eigenvalues_pos, cfc_setIntegral', OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, cfcβ_setIntegral', cfcβ_apply_mem_elemental, wInner_cWeight_const_right, inv_eq_conj, ContinuousMap.elemental_id_eq_top, LinearMap.eq_adjoint_iff_basis_right, IsSelfAdjoint.commute_cfcβ, norm_apply_le_norm_cfcβ, innerββ_apply_coe, LinearMap.orthogonal_range, LinearMap.singularValues_of_lt, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, range_cfcHom, AddChar.map_neg_eq_conj, EuclideanSpace.inner_single_right, nnnorm_cfcHom, integrableOn_cfc, continuousOn_cfc, Submodule.orthogonal_eq_inter, normSq_add, LinearMap.IsPositive.adjoint_eq, fderiv_norm_rpow, ContinuousLinearMap.norm_map_iff_adjoint_comp_self, ContinuousLinearMap.norm_adjoint_comp_self, LinearPMap.mem_adjoint_domain_iff, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, Matrix.l2_opNNNorm_conjTranspose_mul_self, coe_innerββ_apply, HasGradientAt.hasDerivAt, InnerProductSpace.continuousLinearMapOfBilin_apply, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, conj_eq_re_sub_im, inner_matrix_row_row, cfcβL_integrable, conj_ofNat, Matrix.instStarOrderedRing, LinearMap.self_comp_adjoint_injective_iff, ContinuousMap.starSubalgebra_topologicalClosure_eq_top_of_separatesPoints, ContinuousLinearMap.apply_norm_sq_eq_inner_adjoint_right, innerSL_apply_coe, Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitary, ContinuousWithinAt.cfc, MeasureTheory.ContinuousMap.inner_toLp, gradient_eq_deriv, LinearMap.toMatrix_adjoint, Matrix.IsStrictlyPositive.posDef, conj_smul, ContinuousLinearMap.isPositive_adjoint_comp_self, LinearMap.im_inner_adjoint_mul_self_eq_zero, nnnorm_cfcβ_le, Subalgebra.SeparatesPoints.rclike_to_real, norm_innerSL_le, LinearMap.posSemidef_toMatrix_iff, HasGradientWithinAt.hasFDerivWithinAt, hasSum_conj', InnerProductSpace.conj_inner_symm, LinearMap.isAdjointPair_inner, LinearMap.IsPositive.adjoint_conj, range_cfc, LinearIsometryEquiv.toContinuousLinearEquiv_smul, HasGradientAtFilter.hasDerivAtFilter, MeasureTheory.eLpNorm_conj, inner_gradient_right, Real.fourierIntegral_iteratedFDeriv, Matrix.PosDef.posDef_sqrt, norm_cfcβ_le_iff, inner_conj_symm, AddChar.inv_apply_eq_conj, Matrix.IsHermitian.star_eigenvectorUnitary_mulVec, InnerProductSpace.symm_toEuclideanLin_rankOne, ContinuousLinearMap.adjoint_innerSL_apply, ContinuousLinearMap.mem_invtSubmodule_adjoint_iff, normSq_sub, Orthonormal.inner_sum, ContinuousMapZero.nonUnitalStarAlgHom_apply_mul_eq_zero, InnerProductSpaceable.inner_.conj_symm, Matrix.IsHermitian.instContinuousFunctionalCalculus, fderiv_norm_sq_apply, IsSelfAdjoint.commute_cfc, cfcHom_apply_mem_elemental, conj_neg_I, cfc_setIntegral, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, InnerProductSpace.Core.inner_conj_symm, fderiv_norm_sq, Orientation.inner_mul_inner_add_areaForm_mul_areaForm', norm_cfc_lt, ContinuousLinearMap.innerSL_apply_comp, ContinuousLinearMap.toSesqForm_apply_norm_le, LinearMap.adjoint_id, inner_smul_left, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, cfc_integral', ContinuousLinearMap.adjoint_adjoint, restrict_toContinuousMap_eq_toContinuousMapStar_restrict, inner_matrix_col_col, Matrix.IsHermitian.im_star_dotProduct_mulVec_self, normSq_conj, ContinuousLinearMap.orthogonal_ker, InnerProductSpace.norm_rankOne, cfc_mem, Matrix.PosDef.re_dotProduct_pos, LinearMap.IsPositive.conj_adjoint, cfcβ_integral', nnnorm_cfcβ_lt, LinearIsometry.adjoint_comp_self
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