toStar 📖 | CompOp | 1131 mathmath: unitary.spectrum.unitary_conjugate, range_cfcₙ_nnreal, Matrix.l2_opNorm_toEuclideanCLM, ContinuousMapZero.coe_star, NonUnitalSubalgebra.coe_starClosure, continuous_decomposeProdAdjoint, Matrix.posSemidef_conjTranspose_mul_self, StarModule.decomposeProdAdjointL_symm_apply, NonUnitalStarSubalgebra.prod_toNonUnitalSubalgebra, StarModule.selfAdjointPart_add_skewAdjointPart, cfcₙ_def, star_eq_zero, continuous_cfcₙHomSuperset_left, unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, Unitary.conjStarAlgAut_trans_conjStarAlgAut, norm_cfcₙHom, star_mul_star, cfcₙHom_mono, IsStarNormal.instNonUnitalContinuousFunctionalCalculus, Matrix.kroneckerTMulStarAlgEquiv_symm_apply, Complex.coe_realPart, IsIdempotentElem.star_iff, IsStarNormal.one_sub, DoubleCentralizer.star_snd, StarAddMonoid.toStarModuleNNRat, differentiableOn_star_iff, norm_star, Unitary.norm_expUnitary_smul_argSelfAdjoint_sub_one_le, NonUnitalIsometricContinuousFunctionalCalculus.isometric, cfcₙHom_apply_mem_elemental, StarSubalgebra.inclusion_apply, IsUnit.star, CFC.sqrt_eq_one_iff', CFC.posPart_one, Set.image_star, AlgHomClass.instStarHomClass, NonUnitalCStarAlgebra.toStarModule, NonUnitalStarAlgHom.inl_apply, nnnorm_cfcₙ_nnreal_le_iff, realPart_idem, star_ofNat, Matrix.posSemidef_iff_eq_conjTranspose_mul_self, NonUnitalStarAlgebra.mem_bot, IsUnit.isStrictlyPositive_star_right_conjugate_iff, CStarAlgebra.nonneg_iff_exists_isSelfAdjoint_and_eq_mul_self, NonUnitalStarSubalgebra.centralizer_le, NonUnitalStarSubalgebra.topologicalClosure_adjoin_le_centralizer_centralizer, CFC.posPart_natCast, RingHom.star_apply, IsSelfAdjoint.star_mul_self, Matrix.trace_mul_conjTranspose_self_eq_zero_iff, CFC.tendsto_cfc_rpow_sub_one_log, StarSubalgebra.coe_map, Matrix.cstar_nnnorm_def, NonUnitalStarSubsemiring.instNonUnitalSubsemiringClass, realPart_ofReal, spinGroup.coe_star_mul_self, CFC.sq_sqrt, Unitary.conjStarAlgAut_symm, RCLike.star_def, unitary.map_id, BoundedContinuousFunction.mkOfCompact_star, Matrix.isHermitian_conjTranspose_mul_self, Matrix.conjTranspose_sum, pinGroup.coe_star_mul_self, instTrivialStarReal, CentroidHom.star_centerToCentroidCenter, isRightRegular_star_iff, BoundedContinuousFunction.char_neg, val_inv_unitarySubgroupUnitsEquiv_symm_apply_coe, Unitization.real_cfcₙ_eq_cfc_inr, TensorProduct.star_tmul, CliffordAlgebraQuaternion.toQuaternion_star, lp.coeFn_star, imaginaryPart_I_smul, unitary.inv_mul_mem_iff, NumberField.mem_maximalRealSubfield_iff, Matrix.PosSemidef.isHermitian, isClosedEmbedding_cfcₙAux, Complex.star_def, Unitary.conjStarAlgEquiv_unitaryLinearIsometryEquiv, Matrix.posSemidef_self_mul_conjTranspose, selfAdjoint.expUnitaryPathToOne_apply, NonUnitalStarAlgebra.coe_bot, NonUnitalStarAlgebra.mem_top, CFC.nnnorm_sqrt, Subalgebra.star_adjoin_comm, HasSum.matrix_conjTranspose, LinearMap.intrinsicStar_mulRight, CentroidHom.starCenterIsoCentroid_symm_apply_coe, Unitary.mapEquiv_symm_apply, LE.le.star_eq, Module.End.spectrum_intrinsicStar, NonUnitalStarAlgebra.elemental.isClosedEmbedding_coe, Matrix.conjTranspose_mul_self_mulVec_eq_zero, IsUnit.star_right_conjugate_nonneg_iff, IsCHSHTuple.B₀_sa, NonUnitalStarSubalgebra.subsingleton_of_subsingleton, skewAdjoint.isStarNormal_of_mem, StarSubsemiring.mem_toSubsemiring, commute_star_star, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply_comp_toReal, CFC.sqrt_rpow, NonUnitalStarRingHom.coe_zero, Matrix.PosSemidef.sqrt_eq_zero_iff, UnitAddTorus.mFourierSubalgebra_coe, Unitization.starAlgHom_ext_iff, CFC.abs_nnrpow_two, summable_star_iff, instStarModuleNNRealOfReal, RCLike.is_real_TFAE, Pi.star_mulSingle, Matrix.intrinsicStar_toLin', NonUnitalStarSubalgebra.unitizationStarAlgEquiv_apply_coe, LinearMap.toMatrixOrthonormal_reindex, dotProduct_star_self_eq_zero, Matrix.posDef_iff_dotProduct_mulVec, UnitAddTorus.mFourierSubalgebra_closure_eq_top, LinearMap.intrinsicStar_toSpanSingleton, CentroidHom.starCenterIsoCentroid_apply, StarSubalgebra.subtype_comp_inclusion, isSelfAdjoint_iff_isStarNormal_and_spectrumRestricts, Matrix.PosDef.eigenvalues_pos, CFC.negPart_algebraMap, cfcₙHom_nnreal_eq_restrict, star_dotProduct_toMatrix₂_mulVec, selfAdjointPart_comp_subtype_skewAdjoint, Matrix.conjTranspose_natCast_smul, cfcHom_continuous, polynomialFunctions.starClosure_topologicalClosure, Set.nonempty_star, cfcL_apply, WithCStarModule.inner_def, StarAddMonoid.toStarModuleRat, NonUnitalStarAlgebra.mem_sInf, unitary.coe_star_mul_self, deriv.star, star_star, cfcHom_nonneg_iff, Matrix.isHermitian_mul_conjTranspose_self, gelfandStarTransform_naturality, Pi.star_single, gelfandStarTransform_apply_apply, Unitary.inv_mul_mem_iff, Matrix.IsUnit.posSemidef_star_right_conjugate_iff, StarModule.decomposeProdAdjointL_apply, IsCHSHTuple.B₁_sa, cfc_apply_mkD, Set.star_centralizer, instStarModuleNNRealReal, HasStrictFDerivAt.star, Memℓp.star_mem, Set.star_inv', unitary.spectrum.unitary_conjugate', unitary.mem_iff_self_mul_star, HasFDerivAt.star, Unitization.starLift_symm_apply_apply, unitary.star_mul_self_of_mem, Unitization.starLift_apply_apply, Continuous.cfc_nnreal', StarOrderedRing.lt_iff, NonUnitalSubalgebra.starClosure_le_iff, Matrix.PosDef.fromBlocks₁₁, CStarRing.norm_mul_self_le, skewAdjoint.mem_iff, CompactlySupportedContinuousMap.star_apply, star_involutive, RCLike.im_eq_zero_iff_isSelfAdjoint, Matrix.dotProduct_star_self_pos_iff, cfcHom_isClosedEmbedding, StarAlgebra.adjoin_nonUnitalStarSubalgebra, StarSubalgebra.map_map, Unitization.inr_star, selfAdjointPart_comp_subtype_selfAdjoint, fderivWithin_star, Matrix.conjTranspose_inv_intCast_smul, Matrix.conjTranspose_natCast, LE.le.isSelfAdjoint, IsUnit.cfcSqrt, CFC.continuousOn_log, Complex.instContinuousStar, Matrix.PosSemidef.conjTranspose_mul_mul_same, BoundedContinuousFunction.coe_toContinuousMapStarₐ, ContinuousOn.cfc_nnreal', IsGreatest.nnnorm_cfc_nnreal, NonUnitalStarAlgebra.iInf_toNonUnitalSubalgebra, IsSelfAdjoint.add_star_self, NonUnitalStarAlgebra.coe_top, skewAdjoint.instIsStarNormalValMemAddSubgroup, LinearMap.toMatrixOrthonormal_apply_apply, NonUnitalStarAlgebra.coe_sInf, unitary.map_comp, Units.instStarModule, IsSelfAdjoint.mul_star_self, MulChar.star_apply, cfcₙ_apply_mkD, cfcₙHom_id, CStarMatrix.inner_toCLM_conjTranspose_left, Matrix.conjTranspose_sub, Matrix.conjTranspose_eq_diagonal, Matrix.posSemidef_vecMulVec_self_star, Module.End.mem_eigenspace_intrinsicStar_iff, CFC.continuousOn_sqrt, Matrix.star_dotProduct, Matrix.isHermitian_conjTranspose_iff, IsLeftRegular.star, starMulAut_apply, StarOrderedRing.pos_iff, StarAddMonoid.star_add, Pi.single_star, PositiveLinearMap.preGNS_norm_def, IsSelfAdjoint.intCast, star_pos_iff, Matrix.ker_mulVecLin_conjTranspose_mul_self, Matrix.toAlgEquiv_kroneckerStarAlgEquiv, CliffordAlgebra.star_def', Matrix.conjTranspose_permMatrix, starL_apply, unitary.mapEquiv_trans, FreeAlgebra.star_algebraMap, Pi.intrinsicStar_comul_commSemiring, IsStarNormal.cfcₙ_map, CompactlySupportedContinuousMap.coe_star, cfcHom_le_iff, cfcHom_id, Matrix.rank_conjTranspose, Unitary.spectrum_star_left_conjugate, MeasureTheory.MemLp.star, Matrix.PosSemidef.det_sqrt, spinGroup.mul_star_self_of_mem, Set.star_add, range_cfcₙHom, StarSubalgebra.mem_comap, NonUnitalStarSubalgebra.center_toNonUnitalSubalgebra, Matrix.conjTranspose_tsum, Units.mul_inv_mem_unitary, Matrix.PosDef.conjTranspose_mul_mul_same, starRingAut_apply, NonUnitalStarSubalgebra.unitization_range, Matrix.toAlgEquiv_kroneckerTMulStarAlgEquiv, Matrix.dotProduct_star, StarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, star_zsmul, eq_star_iff_eq_star, unitary.mem_iff, NonUnitalStarAlgebra.adjoin_toNonUnitalSubalgebra, Matrix.conjTranspose_kronecker, Unitary.mem_iff_self_mul_star, Matrix.mem_unitaryGroup_iff, HasFDerivWithinAt.star, Matrix.star_dotProduct_star, star_right_conjugate_pos, Commute.cfc_real, CFC.abs_nnrpow, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply_coe, selfAdjoint.imaginaryPart_coe, CliffordAlgebra.star_def, nnnorm_star, nnnorm_cfcₙ_nnreal_lt, CFC.sqrt_eq_rpow, Matrix.conjTranspose_zero, Unitary.map_coe, NonUnitalStarSubsemiring.coe_ofClass, differentiableAt_star_iff, CStarAlgebra.nonneg_iff_isSelfAdjoint_and_negPart_eq_zero, NumberField.ComplexEmbedding.IsConj.eq, cfc_real_eq_nnreal, Matrix.PosSemidef.posSemidef_sqrt, cfcₙHom_integral, mul_star_self_nonneg, NonUnitalStarSubsemiring.instStarMemClass, StarAlgHom.realContinuousMapOfNNReal_apply, star_left_conjugate_pos, CStarAlgebra.isStrictlyPositive_iff_exists_isUnit_and_isSelfAdjoint_and_eq_mul_self, BoundedContinuousFunction.instStarModule, unitary.toUnits_comp_map, StarSubsemiring.toSubsemiring_le_iff, continuous_decomposeProdAdjoint_symm, CentroidHom.star_apply, gelfandStarTransform_symm_apply, IsSelfAdjoint.cfc, StarMul.toStarModule, Matrix.star_vecMul, CStarModule.inner_smul_left_complex, Nat.instTrivialStar, Unitary.star_mul_self_of_mem, HasDerivAt.star, Matrix.conjTranspose_inv_natCast_smul, star_isometry, StarRing.star_add, Matrix.eigenvalues_conjTranspose_mul_self_nonneg, StarAlgebra.adjoin_nonUnitalStarSubalgebra_eq_span, CStarModule.star_inner, Matrix.frobenius_norm_conjTranspose, Matrix.toEuclideanCLM_toLp, WeakDual.CharacterSpace.homeoEval_naturality, realPart.norm_le, CFC.posPart_algebraMap_nnreal, range_cfcₙ, unitary.mem_iff_star_mul_self, Matrix.PosSemidef.sqrt_eq_one_iff, CStarRing.norm_star_mul_self', Units.coe_star, Matrix.PosSemidef.sqrt_sq, RCLike.mul_wInner_left, StarMemClass.star_coe_eq, IsStarNormal.neg, NormedStarGroup.to_continuousStar, IsCHSHTuple.A₁_sa, PositiveLinearMap.preGNS_inner_def, IsStarNormal.val_inv, star_natCast_smul, starL'_apply, cfcₙAux_id, star_intCast, IsStarNormal.zero, StarSubalgebra.subtype_apply, CFC.sqrt_eq_one_iff, IsSelfAdjoint.inr, realPart_add_I_smul_imaginaryPart, CStarAlgebra.norm_posPart_le, Matrix.conjTranspose_zsmul, Matrix.det_conjTranspose, IsGreatest.nnnorm_cfcₙ_nnreal, NonUnitalSubalgebra.mem_star_iff, Matrix.PosSemidef.eq_sqrt_iff_sq_eq, isometry_cfcₙHom, Unitization.starMap_id, CFC.continuous_abs, Unitary.spectrum_star_right_conjugate, StarSubalgebra.isClosedEmbedding_inclusion, NonUnitalStarAlgebra.adjoin_mono, StarSubsemiring.toSubsemiring_injective, gelfandTransform_map_star, dotProduct_star_self_nonneg, polynomialFunctions.starClosure_eq_adjoin_X, continuousOn_cfc_nnreal, Matrix.conjTranspose_nonsing_inv, FreeMonoid.star_one, pinGroup.star_mem, star_neg, FreeAlgebra.star_ι, cfcHom_integral, Matrix.l2_opNorm_conjTranspose_mul_self, Matrix.conjTranspose_swap, StarSubsemiring.coe_toSubsemiring, star_ratCast_smul, Subalgebra.mem_starClosure, Unitary.conjStarAlgAut_ext_iff', star_finsuppProd, cfcₙHom_predicate, cfc_nnreal_eq_real, StarSubsemiring.subsemiringClass, Set.star_inv, CStarRing.star_mul_self_eq_zero_iff, selfAdjoint.star_val_eq, StarModule.decomposeProdAdjoint_symm_apply, Unitization.starLift_range, Matrix.posDef_conjTranspose_iff, StarSubsemiring.mem_carrier, Matrix.PosSemidef.eigenvalues_nonneg, IsSelfAdjoint.log, IsStarProjection.one, ContinuousFunctionalCalculus.exists_cfc_of_predicate, Unitization.inl_star, Matrix.PosSemidef.mul_mul_conjTranspose_same, NonUnitalStarAlgebra.mem_iInf, CFC.abs_natCast, Matrix.adjugate_conjTranspose, CStarAlgebra.isStrictlyPositive_iff_isStrictlyPositive_sqrt_and_eq_sqrt_mul_sqrt, TensorProduct.instStarModule, LDL.lower_conj_diag, IsIdempotentElem.isSelfAdjoint_iff_isStarNormal, star_nnrat_smul, MeasureTheory.eLpNorm_star, NonUnitalStarAlgebra.adjoin_eq_span, Matrix.l2_opNNNorm_conjTranspose, Matrix.conjTranspose_inv_ofNat_smul, IsSelfAdjoint.cfc_arg, NonUnitalStarAlgebra.gc, CliffordAlgebraQuaternion.ofQuaternion_star, NonUnitalStarAlgebra.subset_adjoin, summable_matrix_conjTranspose, NonUnitalStarAlgHom.inr_apply, Unitary.map_comp, LinearMap.IntrinsicStar.isSelfAdjoint_iff_map_star, cfc_def, Unitization.inrNonUnitalStarAlgHom_apply, Unitary.mapEquiv_apply, DoubleCentralizer.star_fst, NormedStarGroup.norm_star_le, Unitization.starMap_inl, fourierSubalgebra_separatesPoints, NonUnitalStarSubalgebra.range_val, StarAlgHom.realContinuousMapOfNNReal_apply_comp_toReal, LinearMap.toMatrixOrthonormal_symm_apply, NonUnitalSubalgebra.starClosure_mono, LinearMap.toMatrix_innerₛₗ_apply, Unitization.starMap_inr, Matrix.eigenvalues_self_mul_conjTranspose_nonneg, star_lt_one_iff, star_inv_intCast_smul, NonUnitalStarAlgebra.elemental.isClosed, CFC.abs_nnrpow_two_mul, Continuous.cfc_nnreal_of_mem_nhdsSet, Matrix.PosSemidef.toLinearMap₂'_zero_iff, NonUnitalStarAlgebra.top_toNonUnitalSubalgebra, Filter.IsIncreasingApproximateUnit.eventually_isSelfAdjoint, NormedSpace.star_exp, IsSelfAdjoint.instNonUnitalContinuousFunctionalCalculus, Matrix.blockDiagonal_conjTranspose, Matrix.l2_opNorm_conjTranspose, Complex.selfAdjointEquiv_apply, IsSelfAdjoint.natCast, Matrix.conjTranspose_eq_natCast, unitary.star_mem, CliffordAlgebra.star_smul, Continuous.cfcₙ_nnreal, Matrix.PosDef.conjTranspose_mul_self, CStarAlgebra.isStrictlyPositive_iff_eq_mul_star_self, HasDerivAtFilter.star, CFC.abs_star, Unitization.isSelfAdjoint_inr, NonUnitalStarAlgebra.range_eq_top, CStarAlgebra.linear_combination_nonneg, NonUnitalStarSubalgebra.unitization_injective, NonUnitalStarSubalgebra.unitization_apply, IsUnit.isStrictlyPositive_star_left_conjugate_iff, NonUnitalStarSubalgebra.coe_centralizer, CStarAlgebra.norm_smul_two_inv_smul_add_four_unitary, Matrix.IntrinsicStar.isSelfAdjoint_toLin'_iff, ContinuousAt.cfcₙ_nnreal, star_mul_self_add_self_mul_star, nonneg_iff_isSelfAdjoint_and_spectrumRestricts, differentiableWithinAt_star_iff, range_cfcₙ_eq_range_cfcₙHom, ContinuousMap.adjoin_id_eq_span_one_union, star_sum, imaginaryPart.norm_le, ContinuousOn.cfc_nnreal_of_mem_nhdsSet, StarSubalgebra.centralizer_toSubalgebra, CFC.abs_algebraMap, NonUnitalStarSubsemiring.instCanLiftSetCoeAndMemOfNatForallForallForallForallHAddForallForallForallForallHMulForallForallStar, Matrix.conjTranspose_kroneckerTMul, Matrix.isHermitian_gram, LinearMap.IsSymmetric.isSymmetric_smul_iff, realPart_comp_subtype_selfAdjoint, TrivialStar.isStarNormal, IsCHSHTuple.A₀_sa, Matrix.conjTranspose_ratCast_smul, Matrix.ofLp_toEuclideanCLM, Matrix.conjTranspose_list_sum, IsStrictlyPositive.nnrpow, Matrix.exp_conjTranspose, Circle.star_addChar, Matrix.kroneckerTMulStarAlgEquiv_apply, StarSubalgebra.star_mem', StarSubalgebra.coe_subtype, isSelfAdjoint_algebraMap_iff, RCLike.instContinuousStar, Ring.inverse_star, ContinuousMapZero.nonUnitalStarAlgHom_precomp_apply, Matrix.conjTranspose_eq_ofNat, starRingEnd_apply, Matrix.isDiag_conjTranspose_iff, inr_comp_cfcₙHom_eq_cfcₙAux, StarAlgebra.star_self_mem_adjoin_singleton, CFC.monotoneOn_one_sub_one_add_inv_real, IsUnit.star_left_conjugate_nonneg_iff, skewAdjoint.negISMul_apply_coe, NonUnitalStarSubsemiring.mem_carrier, Matrix.UnitaryGroup.inv_val, NonUnitalStarSubalgebra.mem_centralizer_iff, ContinuousWithinAt.cfcₙ_nnreal, StarAlgHom.ofId_apply, CommCStarAlgebra.toStarModule, QuasispectrumRestricts.isSelfAdjoint, Unitary.mul_inv_mem_iff, NonUnitalStarAlgebra.elemental.self_mem, CFC.continuousOn_nnrpow, isRegular_star_iff, Summable.star, imaginaryPart_realPart, Matrix.isHermitian_inv, StarAlgebra.star_subset_adjoin, starMulEquiv_apply, star_mul_self_nonneg, Matrix.star_mul, imaginaryPart_eq_neg_I_smul_skewAdjointPart, IsUnit.isSelfAdjoint_conjugate_iff, selfAdjoint.isSelfAdjoint, range_cfcₙ_nnreal_eq_image_cfcₙ_real, StarSubalgebra.map_toSubalgebra, Matrix.posDef_iff_eq_conjTranspose_mul_self, skewAdjointPart_comp_subtype_selfAdjoint, star_nsmul, Filter.Tendsto.cfcₙ_nnreal, Unitary.conjStarAlgAut_apply, WeakDual.CharacterSpace.compContinuousMap_apply, NonUnitalStarAlgHom.coe_zero, starₗᵢ_apply, ContinuousLinearMap.instStarModuleId, RCLike.wInner_smul_left, continuous_cfcHomSuperset_left, IsUnit.cfcNNRpow, unitary.mapEquiv_symm, Matrix.conjTranspose_eq_intCast, Unitary.mem_iff_star_mul_self, star_right_conjugate_lt_conjugate, Unitary.toAlgEquiv_conjStarAlgAut, cfcₙHom_isClosedEmbedding, Subalgebra.coe_star, apply_eq_star_dotProduct_toMatrix₂_mulVec, realPart_I_smul, Matrix.vecMul_conjTranspose_mul_self_eq_zero, SpectrumRestricts.isSelfAdjoint, selfAdjoint.realPart_unitarySelfAddISMul, NonUnitalStarAlgebra.toNonUnitalSubalgebra_eq_top, ContinuousOn.cfc_nnreal, nnnorm_cfcₙ_nnreal_lt_iff, PositiveLinearMap.gnsStarAlgHom_apply, mul_star_self_pos, Matrix.trace_conjTranspose_mul_self_eq_zero_iff, IsSelfAdjoint.of_nonneg, LinearMap.toMatrix'_intrinsicStar, cfcₙHom_le_iff, Matrix.trace_conjTranspose, nnnorm_cfc_nnreal_lt, isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestricts, Matrix.diagonal_conjTranspose, Matrix.conjTransposeAddEquiv_apply, star_injective, imaginaryPart_apply_coe, Matrix.posSemidef_vecMulVec_star_self, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_apply, NonUnitalStarAlgebra.star_subset_adjoin, IsSelfAdjoint.ratCast, IsStrictlyPositive.sqrt, StarSubalgebra.comap_id, CStarRing.norm_star_mul_self, Matrix.PosSemidef.isUnit_sqrt_iff, cfcₙ_real_eq_nnreal, imaginaryPart_comp_subtype_selfAdjoint, nnnorm_cfc_nnreal_le, Subalgebra.starClosure_toSubalgebra, CStarModule.inner_op_smul_left, CStarMatrix.mul_entry_mul_eq_inner_toCLM, ContinuousOn.cfcₙ_nnreal_of_mem_nhdsSet, Matrix.coe_toEuclideanCLM_eq_toEuclideanLin, Matrix.PosSemidef.conjTranspose, one_lt_star_iff, Matrix.rank_self_mul_conjTranspose, star_inv_natCast_smul, Continuous.cfc_nnreal, StarAlgebra.elemental.star_self_mem, cfcHomSuperset_apply, star_lt_star_iff, nnnorm_cfc_nnreal_le_iff, isStarProjection_one_sub_iff, Matrix.conjTransposeRingEquiv_symm_apply, Unitary.coe_isStarNormal, HasFDerivAtFilter.star, LinearMap.toMatrixOrthonormal_apply, CFC.sqrt_sq, cfcₙHom_eq_cfcₙ_extend, IsSelfAdjoint.star_iff, EuclideanSpace.inner_eq_star_dotProduct, NonUnitalSubalgebra.coe_star, NonUnitalCommCStarAlgebra.toStarModule, CFC.rpow_sqrt_nnreal, realPart_surjective, Matrix.conjTranspose_one, star_qsmul, cfc_star_id, ContinuousMapZero.instTrivialStar, Unitary.conjStarAlgAut_symm_apply, spectrum.star_mem_resolventSet_iff, selfAdjoint.star_coe_unitarySelfAddISMul, NonUnitalStarAlgebra.elemental.le_centralizer_centralizer, star_nnqsmul, Unitary.toRingEquiv_conjStarAlgAut, instContinuousStarUnits, NonUnitalStarAlgHom.map_adjoin_singleton, skewAdjoint.star_val_eq, Set.Finite.star, ContinuousMapZero.toContinuousMapHom_toNNReal, Complex.instStarModuleReal, StarSubalgebra.comap_comap, DoubleCentralizer.coeHom_apply, CStarAlgebra.mul_star_le_algebraMap_norm_sq, cfcₙHom_map_quasispectrum, spectrum.map_star, IsSelfAdjoint.instIsometricContinuousFunctionalCalculus, Memℓp.star_iff, fourierSubalgebra_coe, NonUnitalStarSubalgebra.prod_inf_prod, Matrix.conjTranspose_zpow, Matrix.PosDef.fromBlocks₂₂, star_right_conjugate_le_conjugate, star_le_iff, Matrix.toLin_conjTranspose, RCLike.instStarModuleReal, imaginaryPart_surjective, cfcHom_nnreal_eq_restrict, star_eq_iff_star_eq, star_prod, MulChar.star_apply', NonUnitalStarAlgebra.comap_top, NonUnitalStarAlgebra.elemental.star_self_mem, Matrix.PosSemidef.sq_sqrt, unitary.coe_map, spec_cfcₙAux, ContinuousOn.cfcₙ_nnreal', Matrix.norm_conjTranspose, IsRightRegular.star, pinGroup.star_mem_iff, cfcHom_eq_cfc_extend, star_lt_iff, CFC.abs_mul_self, conjugate_lt_conjugate', selfAdjoint.realPart_coe, NonUnitalStarRingHom.zero_apply, HasSum.star, Matrix.isHermitian_add_transpose_self, isLeftRegular_star_iff, star_nnratCast, NNRat.instTrivialStar, LinearMap.instStarModuleId, Unitization.starLift_apply, SpectrumRestricts.starAlgHom_apply, CFC.abs_ofNat, dotProduct_self_star_nonneg, CFC.negPart_one, Matrix.isHermitian_iff_isSymmetric, cfcₙHomSuperset_id, conjugate_lt_conjugate, Matrix.PosSemidef.inv_sqrt, Set.star_mem_center, spinGroup.star_mem, Unitary.toUnits_comp_map, Unitization.starMap_comp, InnerProductSpace.toMatrix_rankOne, NonUnitalStarAlgebra.coe_iInf, CFC.abs_algebraMap_nnreal, StarSubsemiring.starMemClass, CliffordAlgebra.star_ι, UnitAddTorus.mFourierSubalgebra_separatesPoints, Unitary.coe_map_star, Matrix.PosSemidef.dotProduct_mulVec_nonneg, Matrix.isUnit_conjTranspose, CStarRing.norm_self_mul_star, skewAdjointPart_apply_coe, CStarMatrix.ofMatrix_eq_ofMatrixStarAlgEquiv, continuous_selfAdjointPart, Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Matrix.nnnorm_conjTranspose, ContinuousMap.evalStarAlgHom_apply, NonUnitalStarRingHom.map_le_map_of_map_star, Matrix.star_eq_inv, selfAdjointPartL_apply_coe, nnnorm_cfcₙHom, CFC.nnnorm_rpow, Matrix.mulVec_conjTranspose, Matrix.conjTranspose_eq_one, Continuous.cfcₙ_nnreal_of_mem_nhdsSet, ContinuousMap.nonUnitalStarAlgebraAdjoin_id_subset_ker_evalStarAlgHom, cfc_apply, IsStarNormal.instContinuousFunctionalCalculus, LinearMap.intrinsicStar_mulLeft, StarSubalgebra.starModule, one_le_star_iff, CStarAlgebra.star_mul_le_algebraMap_norm_sq, SemiconjBy.star_star_star, NonUnitalStarSubalgebra.mem_center_iff, CStarAlgebra.isStrictlyPositive_iff_isUnit_sqrt_and_eq_sqrt_mul_sqrt, cfc_comp_norm, StarModule.complexToReal, CFC.abs_intCast, apply_le_nnnorm_cfc_nnreal, Matrix.conjTranspose_inj, Matrix.isHermitian_fromBlocks_iff, Matrix.posSemidef_iff_eq_sum_vecMulVec, NonUnitalStarSubalgebra.coe_center, range_cfc_nnreal_eq_image_cfc_real, IsStarNormal.one, Complex.coe_selfAdjointEquiv, Matrix.isHermitian_transpose_add_self, Matrix.vecMul_conjTranspose, StarAlgebra.adjoin_toSubalgebra, Matrix.isHermitian_natCast, isClosedEmbedding_cfcₙHom_of_cfcHom, NonUnitalStarAlgHom.realContinuousMapZeroOfNNReal_injective, IsStarNormal.cfc_map, unitary.coe_map_star, Set.Nonempty.star, conjugate_pos', imaginaryPart_ofReal, star_zero, Matrix.self_mul_conjTranspose_mulVec_eq_zero, NonUnitalSubalgebra.star_mono, LinearMap.intrinsicStarModule, QuasispectrumRestricts.nonUnitalStarAlgHom_apply, StarOrderedRing.le_iff, Unitization.starMap_apply, coe_starₗᵢ, Set.star_subset, NonUnitalContinuousFunctionalCalculus.exists_cfc_of_predicate, Matrix.star_dotProduct_gram_mulVec, Unitization.instIsStarNormal, IsSelfAdjoint.zero, StarAlgHom.realContinuousMapOfNNReal_injective, Unitary.mapEquiv_symm, MulChar.star_eq_inv, NonUnitalStarAlgebra.map_bot, Subalgebra.topologicalClosure_star_comm, StarSubalgebra.coe_centralizer_centralizer, isSelfAdjoint_conjugate_iff_of_isUnit', cfcHom_isStrictlyPositive_iff, Subalgebra.star_mem_star_iff, Matrix.conjTranspose_pow, toMatrix_innerSL_apply, StarSubsemiring.toSubsemiring_inj, Summable.matrix_conjTranspose, StarSemigroup.toOpposite_starModule, Matrix.PosSemidef.re_dotProduct_nonneg, BoundedContinuousFunction.toContinuousMapStarₐ_apply_apply, IsStarNormal.star, CFC.exists_measure_nnrpow_eq_integral_cfcₙ_rpowIntegrand₀₁, LinearMap.intrinsicStar_smulRight, CFC.spectrum_abs, star_id_of_comm, Matrix.IsDiag.conjTranspose, star_left_conjugate_le_conjugate, NonUnitalStarSubalgebra.coe_centralizer_centralizer, Homeomorph.compStarAlgEquiv'_apply, Filter.IsIncreasingApproximateUnit.eventually_star_eq, Matrix.posSemidef_iff_dotProduct_mulVec, cfc_apply_pi, Unitary.conjStarAlgAut_mul_apply, StarSubalgebra.coe_comap, Matrix.conjTranspose_intCast_smul, CStarAlgebra.nonneg_iff_eq_star_mul_self, StarSubalgebra.toSubalgebra_subtype, pinGroup.star_mul_self_of_mem, DifferentiableAt.star_star, NonUnitalStarAlgebra.mem_adjoin_of_mem, ContinuousMapZero.toContinuousMapHom_apply, NonUnitalStarSubalgebra.centralizer_toNonUnitalSubalgebra, skewAdjoint.conjugate', StarOrderedRing.nonneg_iff, cfc_unitary_iff, unitary.toMonoidHom_mapEquiv, Matrix.PosSemidef.dotProduct_mulVec_zero_iff, HasDerivWithinAt.star, Unitary.map_id, CliffordAlgebra.star_algebraMap, BoundedContinuousFunction.star_mem_range_charAlgHom, Complex.selfAdjointEquiv_symm_apply, Int.instTrivialStar, cfcₙAux_mem_range_inr, ContinuousMap.adjoin_id_eq_span_one_add, cfcₙ_norm_sq_nonneg, StarSubalgebra.mem_centralizer_iff, selfAdjointPart_apply_coe, Unitary.mapEquiv_trans, skewAdjointPartL_apply_coe, BoundedContinuousFunction.star_apply, star_div, RingHom.star_def, LinearMap.IntrinsicStar.isSelfAdjoint_iff_toMatrix', IsSelfAdjoint.star_add_self, star_left_conjugate_lt_conjugate, Matrix.specialUnitaryGroup.coe_star, NonUnitalStarAlgebra.adjoin_le_iff, conjugate_nonneg', BoundedContinuousFunction.coe_star, cfcHomSuperset_id, unitary_iff_isStarNormal_and_spectrum_subset_unitary, CStarMatrix.conjTranspose_zero, CStarAlgebra.nonneg_iff_eq_mul_star_self, NonUnitalStarAlgebra.span_eq_toSubmodule, CFC.sqrt_eq_cfc, Matrix.conjTranspose_multiset_sum, unitary.coe_star, CStarAlgebra.isStrictlyPositive_iff_eq_star_mul_self, Matrix.mem_unitaryGroup_iff', Set.star_singleton, Unitary.coe_map, Unitary.mul_star_self_of_mem, realPart_imaginaryPart, Matrix.conjTranspose_ofNat_smul, instTrivialStarNNReal, Filter.Tendsto.cfc_nnreal, selfAdjoint.mem_iff, IsSelfAdjoint.instContinuousFunctionalCalculus, continuousOn_cfcₙ_nnreal, cfcₙHom_continuous, unitary.mul_inv_mem_iff, CFC.abs_sq, LinearMap.intrinsicStar_apply, Subalgebra.coe_starClosure, IsStarNormal.instNonUnitalIsometricContinuousFunctionalCalculus, FreeMonoid.star_of, DifferentiableAt.star, LinearMap.isSelfAdjoint_iff_map_star, StarMul.star_mul, cfcₙHomSuperset_continuous, skewAdjointPart_eq_I_smul_imaginaryPart, StarSubsemiring.ext_iff, isStarProjection_iff_isIdempotentElem_and_isStarNormal, Matrix.conjTranspose_eq_zero, Set.star_mem_star, Rat.instTrivialStar, NonUnitalStarAlgebra.coe_inf, cfcₙ_apply_pi, Matrix.PosDef.mul_mul_conjTranspose_same, IsStrictlyPositive.isSelfAdjoint, NonUnitalStarAlgebra.map_sup, Set.star_subset_star, NonUnitalStarAlgebra.adjoin_eq, Unitization.inrRangeEquiv_apply_coe, Unitization.instStarModule, star_star_mul, CStarAlgebra.isStrictlyPositive_TFAE, fourierSubalgebra_closure_eq_top, CStarAlgebra.isStrictlyPositive_iff_isSelfAdjoint_and_spectrum_pos, derivWithin.star, Matrix.conjTranspose_neg, NonUnitalStarAlgebra.range_id, Unitization.complex_cfcₙ_eq_cfc_inr, StarSubalgebra.one_mem_toNonUnitalStarSubalgebra, LDL.diag_eq_lowerInv_conj, Matrix.conjTranspose_list_prod, NonUnitalStarAlgebra.map_top, CStarAlgebra.norm_negPart_le, fderiv_star, cfcₙ_star, cfcₙ_nnreal_eq_real, CFC.sqrt_algebraMap, CFC.posPart_algebraMap, star_sub, Matrix.self_mul_conjTranspose_mul_eq_zero, CFC.sqrt_one, IsIdempotentElem.star, NonUnitalStarAlgHom.map_adjoin, unitary.mapEquiv_refl, Matrix.isHermitian_zero, CFC.nnrpow_eq_cfcₙ_real, star_le_one_iff, ZeroAtInftyContinuousMap.star_apply, skewAdjoint.conjugate, imaginaryPart_imaginaryPart, IsSelfAdjoint.ofNat, NonUnitalStarAlgebra.star_self_mem_adjoin_singleton, StarSubalgebra.coe_centralizer, nonneg_iff_isSelfAdjoint_and_quasispectrumRestricts, NonUnitalStarAlgebra.elemental.le_iff_mem, Matrix.isHermitian_one, StarSubalgebra.inclusion_injective, Unitary.mem_iff, cfcHom_predicate, Subalgebra.mem_star_iff, tsum_star, Matrix.conjTranspose_single, CFC.negPart_def, NonUnitalStarSubalgebra.center_eq_top, spinGroup.star_mul_self_of_mem, NonUnitalStarSubalgebra.coe_prod, star_right_conjugate_nonneg, StarAddMonoid.toStarModuleNat, CFC.sqrt_rpow_nnreal, WeakDual.Complex.instStarHomClass, instContinuousStarReal, isStarNormal_of_mem_unitary, NonUnitalStarAlgebra.eq_top_iff, nnnorm_cfc_nnreal_lt_iff, Matrix.conjTranspose_vecMulVec, Units.embed_product_star, PositiveLinearMap.instStarHomClassOfLinearMapClassComplexOfOrderHomClass, imaginaryPart_smul, norm_cfcHom, StarAlgebra.adjoin_eq_span, Unitization.norm_splitMul_snd_sq, EuclideanSpace.inner_toLp_toLp, IsSelfAdjoint.nnratCast, Matrix.conjTranspose_mul_self_eq_zero, CFC.norm_rpow, realPart_apply_coe, starLinearEquiv_apply, dotProduct_self_star_eq_zero, Matrix.conjTranspose_rat_smul, commute_star_comm, isSelfAdjoint_smul_of_mem_skewAdjoint, star_finsuppSum, ContinuousMap.ker_evalStarAlgHom_inter_adjoin_id, MonotoneOn.nnnorm_cfc, conjugate_pos, Units.coe_star_inv, DifferentiableOn.star, star_zpow, NonUnitalStarAlgebra.self_mem_adjoin_singleton, Matrix.IsUnit.posSemidef_star_left_conjugate_iff, OrthonormalBasis.toMatrix_orthonormalBasis_self_mul_conjTranspose, NonUnitalStarAlgebra.map_inf, cfcₙL_apply, ContinuousOn.cfcₙ_nnreal, cfcHomSuperset_continuous, cfcₙ_apply_mem_elemental, IsStarNormal.one_add, CFC.posPart_def, NonUnitalStarAlgHom.coe_inr, CFC.nnrpow_eq_rpow, Unitary.conjStarAlgAut_symm_unitaryLinearIsometryEquiv, pinGroup.coe_star, Matrix.conjTransposeRingEquiv_apply, CFC.cfcₙ_rpowIntegrand₀₁_eq_cfcₙ_rpowIntegrand₀₁_one, ContinuousMap.elemental_id_eq_top, Unitization.starLift_range_le, DoubleCentralizer.instStarModule, WeakDual.CharacterSpace.compContinuousMap_comp, star_nonpos_iff, differentiable_star_iff, Complex.im_eq_zero_iff_isSelfAdjoint, LinearMap.isSymm_iff_basis, star_inj, continuousOn_cfc_nnreal_setProd, CStarRing.nnnorm_self_mul_star, Homeomorph.compStarAlgEquiv'_symm_apply, OrthonormalBasis.toMatrix_orthonormalBasis_conjTranspose_mul_self, starRingEquiv_apply, CFC.abs_one, Matrix.vecMul_self_mul_conjTranspose_eq_zero, CentroidHom.starCenterToCentroid_apply, CStarAlgebra.nonneg_TFAE, nnnorm_cfcHom, Matrix.PosSemidef.sqrt_mul_self, Matrix.isHermitian_diagonal_iff, NonUnitalStarAlgHom.coe_inl, realPart_smul, summable_star_iff', cfcₙ_star_id, CFC.abs_mul_abs, NonUnitalStarSubalgebra.prod_top, star_natCast, ContinuousMapZero.elemental_eq_top, ContinuousMapZero.adjoin_id_dense, Matrix.l2_opNNNorm_conjTranspose_mul_self, lp.star_apply, IsRegular.star, Matrix.cstar_norm_def, ContinuousMap.ker_evalStarAlgHom_eq_closure_adjoin_id, CStarAlgebra.toStarModule, CFC.isUnit_nnrpow_iff, Unitization.starLift_symm_apply, isUnit_star, star_div₀, Matrix.isHermitian_transpose_mul_self, star_le_star_iff, selfAdjoint.isStarNormal, star_mul', inner_matrix_row_row, CFC.monotoneOn_cfcₙ_rpowIntegrand₀₁, star_zpow₀, conjugate_le_conjugate', NonUnitalStarAlgebra.sInf_toNonUnitalSubalgebra, Matrix.conjTranspose_mul_self_mul_eq_zero, Unitary.coe_star_mul_self, star_mul_self_pos, Matrix.isHermitian_diagonal, StarSubalgebra.mem_map, StarAlgHom.map_adjoin, Unitary.toMonoidHom_mapEquiv, Matrix.conjTranspose_conjTranspose, IsStarNormal.instIsometricContinuousFunctionalCalculus, cfc_star, IsUnit.mem_unitary_iff_mul_star_self, star_ratCast, Unitary.star_mem_iff, cfcHom_mono, star_invOf, IsometricContinuousFunctionalCalculus.isometric, Matrix.conjTranspose_intCast, Matrix.conjTranspose_smul_self, Matrix.conjTranspose_add, ContinuousAt.cfc_nnreal, NonUnitalSubalgebra.starClosure_toNonUnitalSubalgebra, Unitary.argSelfAdjoint_coe, Matrix.isHermitian_intCast, Matrix.conjTranspose_kronecker', skewAdjoint.I_smul_neg_I, LinearMap.toMatrix_adjoint, CommMonoid.isStarNormal, NonUnitalStarAlgebra.adjoin_le_starAlgebra_adjoin, spinGroup.coe_star, cfcₙHom_of_cfcHom_map_quasispectrum, WeakDual.CharacterSpace.compContinuousMap_id, IsSelfAdjoint.one, ContinuousMapZero.instStarModule, unitary.star_mem_iff, MeasureTheory.AEEqFun.eLpNorm_star, StarSubalgebra.map_id, BoundedContinuousFunction.separatesPoints_charPoly, ContinuousWithinAt.cfc_nnreal, star_nonneg_iff, cfcₙHomSuperset_apply, IsSelfAdjoint.instNonUnitalIsometricContinuousFunctionalCalculus, NonUnitalStarAlgebra.elemental.instCompleteSpaceSubtypeMemNonUnitalStarSubalgebra, starAddEquiv_apply, cfcₙ_apply, nnnorm_cfcₙ_nnreal_le, CFC.sqrt_eq_real_sqrt, Unitary.coe_star, deriv.star', apply_le_nnnorm_cfcₙ_nnreal, Subalgebra.star_mono, skewAdjointPart_comp_subtype_skewAdjoint, HasFDerivAt.star_star, continuousOn_cfcₙ_nnreal_setProd, cfcHom_eq_of_isStarNormal, continuous_skewAdjointPart, Matrix.UnitaryGroup.star_mul_self, Matrix.self_mul_conjTranspose_eq_zero, Matrix.conjTranspose_mul, ContinuousMapZero.coe_toContinuousMapHom, star_mem_iff, CFC.norm_sqrt, Unitary.conjStarAlgAut_star_apply, CFC.continuousOn_rpow, conjugate_nonneg, Matrix.kroneckerStarAlgEquiv_apply, NonUnitalStarAlgHom.subsingleton, cfcHom_map_spectrum, MonotoneOn.nnnorm_cfcₙ, StarSubalgebra.starMemClass, StarSubsemiring.coe_ofClass, Unitization.inrRangeEquiv_symm_apply, NonUnitalStarSubalgebra.mem_prod, StarSubalgebra.isEmbedding_inclusion, cfcₙHom_nonneg_iff, CStarRing.mul_star_self_eq_zero_iff, CFC.nnnorm_nnrpow, Matrix.IsUnit.posDef_star_left_conjugate_iff, IsStarProjection.zero, Unitary.mapEquiv_refl, star_rat_smul, CStarRing.nnnorm_star_mul_self, Matrix.PosDef.posDef_sqrt, Matrix.conjTranspose_injective, star_left_conjugate_nonneg, Matrix.posSemidef_conjTranspose_iff, PositiveLinearMap.gnsNonUnitalStarAlgHom_apply, continuousFunctionalCalculus_map_id, CFC.norm_nnrpow, NonUnitalStarSubalgebra.inclusion_self, StarAddMonoid.toStarModuleInt, Differentiable.star, InnerProductSpace.symm_toEuclideanLin_rankOne, MeasureTheory.Lp.coeFn_star, Commute.cfcₙ_real, Matrix.PosDef.mul_conjTranspose_self, Matrix.frobenius_nnnorm_conjTranspose, Matrix.conjTranspose_ofNat, NonUnitalSubalgebra.mem_starClosure, semiconjBy_star_star_star, Unitary.star_mem, Matrix.rank_conjTranspose_mul_self, IsUnit.mem_unitary_iff_star_mul_self, Unitary.path_apply, Unitary.conjStarAlgAut_ext_iff, HasDerivAt.star_conj, star_one, Set.star_mul, Matrix.IsHermitian.instContinuousFunctionalCalculus, Matrix.PosDef.conjTranspose, star_inv, NonUnitalStarAlgebra.toNonUnitalSubalgebra_bot, cfcHom_apply_mem_elemental, PositiveLinearMap.preGNS_norm_sq, Matrix.kroneckerStarAlgEquiv_symm_apply, Matrix.posSemidef_iff_isHermitian_and_spectrum_nonneg, WeakDual.CharacterSpace.instStarHomClass, pinGroup.mul_star_self_of_mem, NonUnitalStarAlgebra.mem_inf, IsUnit.isSelfAdjoint_conjugate_iff', NonUnitalStarAlgHom.zero_apply, Units.inv_mul_mem_unitary, Matrix.blockDiagonal'_conjTranspose, DifferentiableWithinAt.star, Matrix.dotProduct_self_star_pos_iff, CStarModule.isSelfAdjoint_inner_self, star_inv₀, conjugate_le_conjugate, Unitization.isStarNormal_inr, Matrix.PosSemidef.sqrt_eq_iff_eq_sq, CFC.rpow_eq_cfc_real, star_neg_iff, RCLike.restrict_toContinuousMap_eq_toContinuousMapStar_restrict, Matrix.PosDef.isHermitian, Matrix.mul_self_mul_conjTranspose_eq_zero, inner_matrix_col_col, Matrix.PosDef.dotProduct_mulVec_pos, StarModule.decomposeProdAdjoint_apply, algebraMap_star_comm, Continuous.cfcₙ_nnreal', Matrix.UnitaryGroup.inv_apply, Matrix.conjTranspose_invOf, CStarMatrix.inner_toCLM_conjTranspose_right, CFC.isUnit_sqrt_iff, Matrix.IsUnit.posDef_star_right_conjugate_iff, Matrix.PosDef.re_dotProduct_pos, spinGroup.star_mem_iff, ZeroAtInftyContinuousMap.coe_star, isometry_cfcHom, LinearMap.isSymm_iff_isHermitian_toMatrix, unitary.mul_star_self_of_mem, NonUnitalStarAlgebra.map_iInf, NonUnitalStarAlgebra.inf_toNonUnitalSubalgebra, NonUnitalSubalgebra.star_mem_star_iff, NonUnitalStarAlgebra.adjoin_le_centralizer_centralizer, Matrix.mul_conjTranspose_mul_self_eq_zero, Matrix.conjTranspose_nsmul, isSelfAdjoint_conjugate_iff_of_isUnit, Matrix.star_mulVec, Commute.star_star, HasStrictDerivAt.star, CFC.rpow_sqrt, star_pow, IsSelfAdjoint.cfcₙ, star_intCast_smul, NNReal.instContinuousStar, NonUnitalSubalgebra.star_adjoin_comm
|