ker 📖 | CompOp | 432 mathmath: lTensor_ker_subtype_tensorKerEquiv_symm, Module.FinitePresentation.fg_ker, LieDerivation.IsKilling.ad_mem_ker_killingForm_ad_range_of_mem_orthogonal, ker_le_of_iterateMapComap_eq_succ, groupCohomology.isoCocycles₁_hom_comp_i_apply, map_le_map_iff, Module.End.exists_ker_pow_eq_ker_pow_succ, ker_coprod_of_disjoint_range, ker_eq_top, Polynomial.disjoint_ker_aeval_of_isCoprime, BilinForm.ker_restrict_eq_of_codisjoint, ker_pi, injective_restrict_iff_disjoint, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_apply, ContinuousLinearMap.ker_codRestrict, Algebra.Extension.H1Cotangent.equiv_apply, ImplicitFunctionData.isCompl_ker, IsIdempotentElem.range_eq_ker, le_ker_iff_comp_subtype_eq_zero, tensorKer_tmul, IsIdempotentElem.commute_iff, ContinuousLinearEquiv.snd_equivOfRightInverse, RootPairing.rootSpan_dualAnnihilator_le_ker_rootForm, Module.Flat.ker_lTensor_eq, Module.Relations.Solution.injective_fromQuotient_iff_ker_π_eq_span, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_i_hom, ContinuousLinearMap.ker_le_ker_iff_range_le_range, Submodule.exists_le_ker_of_lt_top, Module.Basis.flag_le_ker_dual, LieModule.lowerCentralSeries_one_inf_center_le_ker_traceForm, tensorKer_coe, Fintype.linearIndependent_iff', ContinuousLinearMap.IsIdempotentElem.ext_iff, SimpleGraph.card_connectedComponent_eq_finrank_ker_toLin'_lapMatrix, ker_localizedMap_eq_localized'_ker, ker_inf_lt_ker_inf_of_map_eq_of_lt, rank_eq_of_surjective, Ideal.mem_toCotangent_ker, eventually_iSup_ker_pow_eq, IsIdempotentElem.ext_iff, LieAlgebra.IsKilling.ker_traceForm_eq_bot_of_isCartanSubalgebra, groupHomology.isoCycles₁_inv_comp_iCycles_apply, ker_restrictScalars, linearIndependent_iff_ker, ContinuousLinearMap.isComplete_ker, LieHom.quotKerEquivRange_toFun, iInf_ker_proj, ker_localizedMap_eq_localized₀_ker, range_domRestrict_eq_range_iff, sub_mem_ker_iff, RootPairing.disjoint_corootSpan_ker_corootForm, LieIdeal.coe_killingCompl_top, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_zero_iff, Finsupp.iInf_ker_lapply_le_bot, groupCohomology.mapCocycles₂_comp_i_apply, Submodule.ker_subtype, ker_eq_bot, iInf_ker_proj_le_iSup_range_single, ker_smul', Submodule.coe_isComplEquivProj_symm_apply, ker_id, ContinuousLinearMap.closedComplemented_ker_of_rightInverse, RootPairing.ker_copolarization_eq_ker_corootForm, ker_linearProjOfIsCompl, KaehlerDifferential.kerTotal_eq, Matrix.ker_mulVecLin_conjTranspose_mul_self, isIdempotentElem_iff_eq_isCompl_projection_range_ker, LocalizedModule.mem_ker_mkLinearMap_iff, ContinuousLinearMap.IsIdempotentElem.ker_mem_invtSubmodule, IsRefl.ker_eq_bot_iff_ker_flip_eq_bot, Algebra.Extension.H1Cotangent.val_zero, RootPairing.exist_set_root_not_disjoint_and_le_ker_coroot'_of_invtSubmodule, tensorKerEquivOfSurjective_symm_tmul, IsProj.eq_conj_prodMap, ContinuousLinearMap.iInf_ker_proj, DirectSum.ker_lmap, Submodule.ker_inl, toKerLocalized_isLocalizedModule, isUnit_iff_ker_eq_bot, bot_lt_ker_of_det_eq_zero, IsIdempotentElem.ker_eq_range, isCompl_iSup_ker_pow_iInf_range_pow, ker_rangeRestrict, Submodule.range_fg_iff_ker_cofg, Function.Exact.linearMap_ker_eq, Submodule.exists_le_ker_of_notMem, ContinuousLinearMap.isClosed_ker, IsIdempotentElem.ker_mem_invtSubmodule_iff, IsProj.isCompl, localized'_ker_eq_ker_localizedMap, IsIdempotentElem.ker_toSpanSingleton_eq_span, IsIdempotentElem.eq_isCompl_projection, ContinuousLinearMap.ker_closedComplemented_of_finiteDimensional_range, Submodule.dualRestrict_ker_eq_dualAnnihilator, Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_iff, Finsupp.ker_mapRange, iSup_range_single_eq_iInf_ker_proj, Matrix.ker_mulVecLin_eq_bot_iff, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, ker_eq_bot_iff_range_eq_top_of_finrank_eq_finrank, ker_prodMap, comap_leq_ker_subToSupQuotient, Submodule.LinearDisjoint.linearIndependent_right_of_flat, LieModule.coe_genWeightSpaceOf_zero, SimpleGraph.linearIndependent_lapMatrix_ker_basis_aux, Module.End.ker_pow_eq_ker_pow_finrank_of_le, ker_toSpanSingleton, LieAlgebra.mem_ker_killingForm_of_mem_rootSpace_of_forall_rootSpace_neg, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_zero_iff, Module.Basis.flag_le_ker_coord, HasStrictFDerivAt.map_implicitFunction_eq, Module.Basis.toDual_ker, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_assoc_apply, BilinForm.apply_apply_same_eq_zero_iff, disjoint_ker, range_dualMap_eq_dualAnnihilator_ker, ker_codRestrict, HasStrictFDerivAt.implicitToPartialHomeomorph_self, ker_toAddSubmonoid, CharacterModule.intSpanEquivQuotAddOrderOf_symm_apply_coe, KaehlerDifferential.range_mapBaseChange, ker_prod_ker_le_ker_coprod, CharacterModule.intSpanEquivQuotAddOrderOf_apply, Polynomial.sup_ker_aeval_eq_ker_aeval_mul_of_coprime, ker_comp, ContinuousLinearMap.coe_projKerOfRightInverse_apply, groupHomology.mapCycles₁_comp_i_apply, ContinuousLinearMap.IsStarNormal.ker_adjoint_eq_ker, ContinuousLinearMap.IsIdempotentElem.isSymmetric_iff_orthogonal_range, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_iff, KaehlerDifferential.ker_map, ClosedSubmodule.orthogonal_eq_inter, IsIdempotentElem.range_eq_ker_one_sub, ModuleCat.kernelIsoKer_inv_kernel_ι_apply, separatingRight_iff_flip_ker_eq_bot, BilinForm.inf_orthogonal_self_le_ker_restrict, IsLocalizedModule.subsingleton_iff_ker_eq_top, CategoryTheory.ShortComplex.Exact.moduleCat_range_eq_ker, span_singleton_sup_ker_eq_top, SimpleGraph.top_le_span_range_lapMatrix_ker_basis_aux, IsLocalizedModule.mem_ker_iff, groupCohomology.isoCocycles₁_inv_comp_iCocycles_apply, ContinuousLinearMap.IsStarNormal.orthogonal_range, lift_rank_eq_of_surjective, ContinuousLinearMap.IsIdempotentElem.TFAE, Matrix.ker_mulVecLin_transpose_mul_self, LocalizedModule.subsingleton_iff_ker_eq_top, ker_toSpanSingleton_eq_bot_iff, HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorph_target, linearIndepOn_iff_disjoint, IsIdempotentElem.ker_toSpanSingleton_one_sub_eq_span, IsIdempotentElem.commute_iff_of_isUnit, Matrix.ker_toLin_eq_bot, ModuleCat.ker_eq_bot_of_mono, LinearMapClass.ker_eq_bot, range_inl, ker_domRestrict, Submodule.disjoint_ker_of_finrank_le, ker_eq_bot', iterateKer_coe, BilinForm.nondegenerate_restrict_iff_disjoint_ker, BilinForm.nondegenerate_iff_ker_eq_bot, Submodule.ker_inclusion, RootPairing.isCompl_rootSpan_ker_rootForm, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_liftK_hom, RootPairing.rootForm_self_eq_zero_iff, groupCohomology.d₀₁_ker_eq_invariants, HasStrictFDerivAt.to_implicitFunction, Subalgebra.LinearDisjoint.mulRightMap_ker_eq_bot_iff_linearIndependent, ker_eq_range_of_comp_eq_id, IsIdempotentElem.isSymmetric_iff_isOrtho_range_ker, groupHomology.isoCycles₂_hom_comp_i_apply, groupCohomology.isoCocycles₂_inv_comp_iCocycles_apply, LinearEquiv.ker_comp, Module.isTorsionBySet_iff_subseteq_ker_lsmul, Module.End.mem_genEigenspace_top, InnerProductSpace.nullSubmodule_le_ker_toDualMap_left, ker_snd, Module.End.genEigenspace_one, Ideal.ker_tensorProductMk_quotient, Submodule.annihilator_span_singleton, VonNeumannAlgebra.IsIdempotentElem.mem_iff, hasEigenvalue_zero_tfae, RootPairing.iInf_ker_root'_eq, mem_ker, SmoothBumpCovering.embeddingPiTangent_ker_mfderiv, groupHomology.π_comp_H1Iso_hom_apply, Matrix.ker_toLin'_eq_bot_iff, Module.FaithfullyFlat.range_le_ker_of_exact_rTensor, quotKerEquivRange_symm_apply_image, rTensor_mkQ, Submodule.IsCompl.projection_ker, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_assoc_apply, LieModuleHom.ker_toSubmodule, IsSemisimpleModule.jacobson_le_ker, IsIdempotentElem.comp_eq_left_iff, IsIdempotentElem.isSymmetric_iff_orthogonal_range, RootPairing.iInf_ker_coroot'_eq, Module.End.eigenspace_def, Module.Relations.Solution.isPresentation_iff, quotKerEquivRange_apply_mk, Matrix.ker_diagonal_toLin', groupHomology.isoCycles₁_hom_comp_i_apply, range_dualMap_eq_dualAnnihilator_ker_of_surjective, CategoryTheory.ShortComplex.exact_iff_surjective_moduleCatToCycles, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_descH_hom, Algebra.Extension.h1Cotangentι_ext_iff, Module.Basis.SmithNormalForm.le_ker_coord_of_notMem_range, LieHom.quotKerEquivRange_invFun, Module.isTorsionBy_iff_mem_ker_lsmul, eventually_isCompl_ker_pow_range_pow, Module.End.eventually_disjoint_ker_pow_range_pow, ModuleCat.kernelIsoKer_hom_ker_subtype, Representation.ker_leftRegular_norm_eq, ContinuousLinearMap.ker_prod, CategoryTheory.ShortComplex.moduleCatCyclesIso_hom_i_assoc_apply, Algebra.Extension.H1Cotangent.val_add, ker_eq_bot_of_cancel, Rep.FiniteCyclicGroup.groupHomologyπEven_eq_zero_iff, Algebra.Extension.H1Cotangent.val_smul, RootPairing.orthogonal_corootSpan_eq, Module.eval_ker, RootPairing.ker_rootForm_eq_dualAnnihilator, AddMonoidHom.coe_toIntLinearMap_ker, LocallyConstant.ker_comapₗ, BilinForm.orthogonal_span_singleton_eq_toLin_ker, Module.Relations.ker_toQuotient, DFinsupp.ker_mapRangeLinearMap, disjoint_ker_iff_injOn, Submodule.ker_subtypeL, lift_rank_range_add_rank_ker, Submodule.annihilator_span, Module.End.genEigenspace_zero_nat, Algebra.Generators.disjoint_ker_toKaehler_of_linearIndependent, CategoryTheory.ShortComplex.moduleCat_exact_iff_ker_sub_range, ker_dualMap_eq_dualCoannihilator_range, groupHomology.isoCycles₂_inv_comp_iCycles_apply, Module.End.eigenspace_div, ModuleCat.kernelIsoKer_hom_ker_subtype_apply, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_self, IsProj.eq_conj_prod_map', ker_zero, ContinuousLinearMap.projKerOfRightInverse_comp_inv, range_inr, Submodule.ker_starProjection, disjoint_ker_of_nondegenerate_restrict, Polynomial.sup_ker_aeval_le_ker_aeval_mul, CategoryTheory.ShortComplex.π_moduleCatCyclesIso_hom_apply, Module.FinitePresentation.out, MvPolynomial.ker_evalₗ, ContinuousLinearMap.IsIdempotentElem.commute_iff_of_isUnit, Representation.FiniteCyclicGroup.coinvariantsKer_leftRegular_eq_ker, exact_subtype_ker_map, Rep.FiniteCyclicGroup.groupCohomologyπEven_eq_iff, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_fst, Algebra.Extension.H1Cotangent.map_apply_coe, map_coe_ker, Submodule.coe_dualAnnihilator_span, HasStrictFDerivAt.implicitToOpenPartialHomeomorph_apply_ker, Submodule.ker_orthogonalProjection, IsIdempotentElem.isCompl, Polynomial.mem_ker_modByMonic, ContinuousLinearMap.orthogonal_range, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_norm, ContinuousLinearMap.IsIdempotentElem.commute_iff, quotKerEquivOfSurjective_symm_apply, LinearIndependent.repr_ker, ker_prod, Submodule.CoFG.ker, Module.End.eigenspace_zero, IsProj.codRestrict_ker, ContinuousLinearMap.projKerOfRightInverse_apply_idem, ContinuousLinearMap.IsIdempotentElem.ker_eq_range, groupCohomology.mapCocycles₁_comp_i_apply, BilinForm.orthogonal_top_eq_ker, isClosed_or_dense_ker, RootPairing.rootSpan_dualAnnihilator_map_eq_iInf_ker_root', Algebra.Extension.h1Cotangentι_apply, isCoatom_ker_of_surjective, IsSymmetric.orthogonal_range, ker_sup_ker_le_ker_comp_of_commute, Module.End.genEigenspace_div, ker_compLeft, CategoryTheory.ShortComplex.moduleCat_exact_iff_range_eq_ker, range_dualMap_eq_dualAnnihilator_ker_of_subtype_range_surjective, ker_le_iff, Submodule.map_strict_mono_or_ker_sup_lt_ker_sup, KaehlerDifferential.ker_map_of_surjective, Rep.FiniteCyclicGroup.groupHomologyπOdd_eq_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_K, ContinuousLinearMap.IsIdempotentElem.range_eq_ker, eqLocus_eq_ker_sub, groupCohomology.π_comp_H2Iso_hom_apply, Module.Basis.flag_le_ker_coord_iff, ker_fst, Module.End.ker_aeval_ring_hom'_unit_polynomial, TopModuleCat.kerι_apply, Module.End.genEigenspace_nat, Module.ker_algebraMap_end, Rep.FiniteCyclicGroup.leftRegular.range_norm_eq_ker_applyAsHom_sub, ker_eq_bot_of_injective, range_dualMap_le_dualAnnihilator_ker, groupCohomology.π_comp_H1Iso_hom_apply, continuous_iff_isClosed_ker, IsCoercive.ker_eq_bot, ContinuousLinearMap.ker_prod_ker_le_ker_coprod, ker_le_ker_comp, Module.End.mem_genEigenspace_nat, MeasureTheory.Lp.ker_toTemperedDistributionCLM_eq_bot, ContinuousLinearMap.completeSpace_ker, Submodule.ker_mkQ, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_apply, groupHomology.π_comp_H2Iso_hom_apply, Module.Relations.Solution.span_relation_le_ker_π, Module.Dual.finrank_ker_add_one_of_ne_zero, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_π_hom, OpenPartialHomeomorph.MDifferentiable.ker_mfderiv_eq_bot, ker_id_sub_eq_of_proj, TensorProduct.map_ker, ker_eq_bot_iff_range_eq_top, iSup_range_single_le_iInf_ker_proj, ker_restrict, eventually_codisjoint_ker_pow_range_pow, groupHomology.mapCycles₂_comp_i_apply, RootPairing.corootSpan_dualAnnihilator_le_ker_rootForm, map_eq_top_iff, injective_domRestrict_iff, CategoryTheory.ShortComplex.moduleCatLeftHomologyData_H, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_assoc_apply, BilinForm.toLin_restrict_ker_eq_inf_orthogonal, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_π_apply, Module.End.ker_pow_le_ker_pow_finrank, LieAlgebra.IsKilling.ker_restrict_eq_bot_of_isCartanSubalgebra, Module.FinitePresentation.fg_ker_iff, Submodule.range_ker_disjoint, Finsupp.lsingle_range_le_ker_lapply, isCompl_of_proj, ModuleCat.mono_iff_ker_eq_bot, groupHomology.π_comp_H1Iso_inv_apply, HasStrictFDerivAt.mem_implicitToPartialHomeomorph_source, separatingLeft_iff_ker_eq_bot, groupCohomology.isoCocycles₂_hom_comp_i_apply, KaehlerDifferential.range_kerCotangentToTensor, HasStrictFDerivAt.implicitToPartialHomeomorph_fst, HasStrictFDerivAt.mem_implicitToPartialHomeomorph_target, BilinForm.Nondegenerate.ker_eq_bot, Submodule.orthogonal_eq_inter, CategoryTheory.ShortComplex.toCycles_moduleCatCyclesIso_hom_assoc_apply, isSMulRegular_on_submodule_iff_disjoint_ker_lsmul_submodule, linearProjOfIsCompl_of_proj, LieHom.ker_toSubmodule, Submodule.ker_inr, Module.exists_ker_toSpanSingleton_eq_annihilator, Submodule.linearProjOfIsCompl_ker, not_hasEigenvalue_zero_tfae, exact_iff, RootPairing.disjoint_rootSpan_ker_rootForm, ContinuousLinearMap.ker_coprod_of_disjoint_range, tensorKerEquiv_apply, IsIdempotentElem.ker_eq_range_one_sub, disjoint_ker', isSMulRegular_iff_ker_lsmul_eq_bot, LinearEquiv.ker, NumberField.mixedEmbedding.disjoint_span_commMap_ker, Module.End.mem_genEigenspace, Finsupp.ker_lsingle, ker_lsmul, ker_le_range_iff, IsIdempotentElem.ker_mem_invtSubmodule, Ideal.map_toCotangent_ker, range_le_ker_iff, RootPairing.isCompl_corootSpan_ker_corootForm, comp_ker_subtype, dualCoannihilator_range_eq_ker_flip, Submodule.LinearDisjoint.linearIndependent_left_of_flat, LieAlgebra.IsKilling.ker_killingForm_eq_bot, RootPairing.corootSpan_dualAnnihilator_map_eq_iInf_ker_coroot', ker_single, finrank_range_add_finrank_ker, ModuleCat.kernelIsoKer_inv_kernel_ι, Polynomial.ker_modByMonicHom, le_ker_iff_map, ContinuousLinearMap.apply_val_ker, Subalgebra.LinearDisjoint.mulLeftMap_ker_eq_bot_iff_linearIndependent_op, HasStrictFDerivAt.implicitFunction_apply_image, ker_eq_bot_of_inverse, Finsupp.lmapDomain_disjoint_ker, ker_tensorProductMk, orthogonal_span_singleton_eq_to_lin_ker, ker_dualMap_eq_dualAnnihilator_range, lTensor_mkQ, ContinuousLinearEquiv.fst_equivOfRightInverse, ker_toAddSubgroup, Submodule.comap_bot, RootPairing.ker_corootForm_eq_dualAnnihilator, Module.Relations.Solution.IsPresentation.ker_π, HasStrictFDerivAt.implicitToPartialHomeomorph_apply_ker, Submodule.mem_invtSubmodule_reflection_iff, graph_eq_ker_coprod, Algebra.Generators.H1Cotangent.equiv_apply, ContinuousLinearEquiv.equivOfRightInverse_symm_apply, ker_le_ker_of_range, ModuleCat.toKernelSubobject_arrow, Module.End.eigenspace_aeval_polynomial_degree_1, Algebra.Extension.Cotangent.ker_mk, ContinuousLinearMap.IsIdempotentElem.ker_mem_invtSubmodule_iff, Module.Basis.eval_ker, RootPairing.ker_polarization_eq_ker_rootForm, quotKerEquivOfSurjective_apply_mk, CategoryTheory.ShortComplex.moduleCatCyclesIso_inv_iCycles_apply, groupHomology.π_comp_H2Iso_inv_apply, IsSimpleModule.ker_toSpanSingleton_isMaximal, HasStrictFDerivAt.mem_implicitToOpenPartialHomeomorph_source, Rep.FiniteCyclicGroup.leftRegular.range_applyAsHom_sub_eq_ker_linearCombination, HasStrictFDerivAt.eq_implicitFunction, rank_range_add_rank_ker, exists_map_addHaar_eq_smul_addHaar', Rep.FiniteCyclicGroup.groupCohomologyπOdd_eq_zero_iff, SimpleGraph.mem_ker_toLin'_lapMatrix_of_connectedComponent, RootPairing.orthogonal_rootSpan_eq, linearIndepOn_iff_linearCombinationOn, toKerIsLocalized_apply_coe, InnerProductSpace.nullSubmodule_le_ker_toDualMap_right, ContinuousLinearMap.orthogonal_ker, IsRefl.ker_flip, ker_smul, surjective_domRestrict_iff, ker_toContinuousLinearMap, ker_le_comap, dualAnnihilator_ker_eq_range_flip, Submodule.comap_map_eq
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