End 📖 | CompOp | 411 mathmath: AlgEquiv.moduleEndSelfOp_apply_apply, Basis.end_repr_apply, LinearMap.exists_monic_and_aeval_eq_zero, End.exists_ker_pow_eq_ker_pow_succ, LinearMap.isNilRegular_iff_natTrailingDegree_charpoly_eq_nilRank, End.smul_def, End.HasEigenvalue.mem_spectrum, LieModule.toEnd_pow_apply_map, End.HasUnifEigenvector.pow_apply, End.iterate_succ', LieModule.trace_toEnd_eq_zero_of_mem_lcs, LieAlgebra.mapsTo_toEnd_genWeightSpace_add_of_mem_rootSpace, Representation.asAlgebraHom_single, LieAlgebra.finrank_engel, skewAdjointLieSubalgebraEquiv_apply, LinearEquiv.conj_trans, Algebra.lmul_algebraMap, LinearEquiv.conj_apply_apply, LinearEquiv.conjAlgEquiv_symm_apply_apply, End.spectrum_intrinsicStar, LieAlgebra.isRegular_iff_natTrailingDegree_charpoly_eq_rank, LieModule.exists_genWeightSpace_zero_le_ker_of_isNoetherian, LinearEquiv.map_mem_invtSubmodule_conj_iff, End.isFinitelySemisimple_sub_algebraMap_iff, LinearMap.mem_isPairSelfAdjointSubmodule, NonUnitalAlgHom.coe_lmul_eq_mul, AlgEquiv.linearEquivConj_mulLeft, PiToModule.fromEnd_apply, LieSubalgebra.toEnd_eq, LieModule.isNilpotent_toEnd_genWeightSpace_zero, LinearMap.charpoly_nilpotent_tfae, End.mul_eq_comp, End.one_eq_id, IsLocalizedModule.iso_apply_mk, isStablyFiniteRing_iff_injective_of_surjective, End.intCast_apply, skewAdjointLieSubalgebraEquiv_symm_apply, End.apply_smulCommClass', Matrix.Represents.smul, Algebra.lmul_injective, LieModule.trace_toEnd_genWeightSpace, Algebra.IsCentral.instEnd, AlgHom.mulLeftRightMatrix.inv_comp, LieModule.shiftedGenWeightSpace.toEnd_eq, endTensorEndAlgHom_apply, LinearMap.mem_skewAdjointSubmodule, LinearEquiv.conj_comp, End.mem_invtSubmodule_iff_mapsTo, End.instLieModule, LinearEquiv.conj_refl, LieSubmodule.Quotient.toEnd_comp_mk', RootPairing.Equiv.weightHom_toLinearMap, LinearEquiv.conjAlgEquiv_apply, LieModule.instIsTriangularizableSubtypeEndMemLieSubalgebraRangeToEnd, LieModule.mem_posFittingCompOf, LocalizedModule.divBy_mul_by, End.maxGenEigenspace_eq_maxGenEigenspace_zero, End.ringHomEndFinsupp_apply_apply, IsSimpleRing.exists_ringEquiv_matrix_end_mulOpposite, LieModule.isNilpotent_range_toEnd_iff, LieAlgebra.rank_le_natTrailingDegree_charpoly_ad, CliffordAlgebra.foldr'Aux_foldr'Aux, End.mem_eigenspace_intrinsicStar_iff, LieSubmodule.lie_top_eq_of_span_sup_eq_top, PiToModule.fromEnd_injective, LinearMap.baseChange_one, Representation.leftRegular_norm_eq_zero_iff, LieAlgebra.ad_eq_lmul_left_sub_lmul_right, LinearMap.isIdempotentElem_map_one_iff, RingEquiv.moduleEndSelf_symm_apply, LieModule.isNilpotent_toEnd_of_isNilpotent, LieAlgebra.hasCentralRadical_and_of_isIrreducible_of_isFaithful, LinearMap.IsProj.eq_conj_prodMap, End.HasEigenvalue.pow, LieSubmodule.coe_map_toEnd_le, QuadraticMap.associated_apply, LieModule.mem_genWeightSpace, LinearMap.baseChange_pow, LinearMap.polyCharpoly_baseChange, LieSubalgebra.toEnd_mk, End.intCast_def, preReflection_apply_self, Matrix.toLpLin_symm_pow, LinearMap.polyCharpolyAux_map_eval, preReflection_preReflection, Basis.end_apply_apply, Matrix.isRepresentation.toEnd_represents, LieModule.exists_genWeightSpace_le_ker_of_isNoetherian, End.hasUnifEigenvalue_iff_mem_spectrum, LieModule.coe_genWeightSpaceOf_zero, LinearEquiv.symm_conjAlgEquiv, End.HasEigenvector.apply_eq_smul, IsSimpleModule.algebraMap_end_bijective_of_isAlgClosed, LieAlgebra.engel_isBot_of_isMin.lieCharpoly_map_eval, End.isNilpotent_iff_of_finite, LieSubmodule.traceForm_eq_zero_of_isTrivial, lieEquivMatrix'_apply, LieModule.weight_vector_multiplication, End.ker_pow_eq_ker_pow_finrank_of_le, LieSubalgebra.coe_ad_pow, isLocalizedModule_iff, LinearMap.tensorProductEnd_apply, End.pow_apply, RootPairing.GeckConstruction.trace_toEnd_eq_zero, LieModule.IsTriangularizable.maxGenEigenspace_eq_top, End.rTensorAlgHom_apply_apply, LieModule.isFaithful_iff, End.IsSemisimple.pow, LinearMap.charpoly_eq_X_pow_iff, RingEquiv.moduleEndSelfOp_apply, VertexOperator.ncoeff_apply, IsAzumaya.mulLeftRight_comp_congr, LieSubmodule.toEnd_comp_subtype_mem, Matrix.Represents.zero, Representation.norm_ofMulDistribMulAction_eq, LieAlgebra.ad_nilpotent_of_nilpotent, AlgHom.mulLeftRight_apply, LieModule.rank_eq_natTrailingDegree, End.aeval_apply_of_hasEigenvector, IsAzumaya.bij, fwdDiff_aux.shiftₗ_pow_apply, IsSemisimpleRing.exists_algEquiv_pi_matrix_end_mulOpposite, LieAlgebra.ad_pow_lie, LinearMap.toMatrix'_algebraMap, End.coe_pow, QuadraticMap.associated_toQuadraticMap, LieModule.isNilpotent_toEnd_of_isNilpotent₂, LinearMap.isAdjointPair_one, DistribMulAction.toModuleEnd_apply, LieSubmodule.mapsTo_pow_toEnd_sub_algebraMap, IsLocalizedModule.fromLocalizedModule_mk, Basis.end_apply, End.ringEquivEndFinsupp_apply_apply_apply, End.isSemisimple_sub_algebraMap_iff, Polynomial.aeval_apply_smul_mem_of_le_comap, End.invtSubmodule.one, RingEquiv.moduleEndSelf_apply, LinearEquiv.conj_apply, Matrix.isRepresentation.toEnd_exists_mem_ideal, Representation.asAlgebraHom_single_one, End.isUnit_iff, LieModule.exists_forall_pow_toEnd_eq_zero, JacobsonNoether.exist_pow_eq_zero_of_le, End.IsSemisimple.aeval, Algebra.lsmul_injective, LinearMap.polyCharpolyAux_map_eq_charpoly, LinearMap.polyCharpolyAux_eval_eq_toMatrix_charpoly_coeff, LieSubmodule.toEnd_restrict_eq_toEnd, LieModule.IsFaithful.injective_toEnd, End.coe_mul, LinearEquiv.conjRingEquiv_apply_apply, Basis.baseChange_end, addMonoidEndRingEquivInt_apply, LinearMap.lTensor_mul, algebraMap_end_eq_smul_id, AlgEquiv.toLinearMapHom_apply_apply, LieModule.trace_comp_toEnd_genWeightSpace_eq, End.lie_apply, End.mem_center_iff, LinearEquiv.conj_symm_conj, killingForm_apply_apply, LinearMap.toMatrix_algebraMap, LieSubalgebra.mem_engel_iff, End.mem_genEigenspace_top, LieModule.iterate_toEnd_mem_lowerCentralSeries₂, Submodule.isIdempotentElemEquiv_apply_coe, End.genEigenspace_one, LinearMap.det_map, LinearMap.hasEigenvalue_zero_tfae, IsSl2Triple.HasPrimitiveVectorWith.pow_toEnd_f_eq_zero_of_eq_nat, LieModule.toEnd_eq_iff, LinearMap.instIsStablyFiniteRingEnd, LinearEquiv.lieConj_apply, LieModule.isNilpotent_toEnd_of_mem_rootSpace, Invertible.toModuleEnd_bijective, Matrix.represents_iff, End.natCast_def, LinearMap.isPairSelfAdjoint_equiv, Matrix.Represents.congr_fun, LinearMap.isIdempotentElem_apply_one_iff, IsAzumaya.coe_tensorEquivEnd, LinearMap.charpoly_constantCoeff_eq_zero_iff, QuadraticMap.half_moduleEnd_apply_eq_half_smul, LieModule.toEnd_lie, End.mem_subsemigroupCenter_iff, End.isRoot_of_hasEigenvalue, IsSimpleRing.exists_algEquiv_matrix_end_mulOpposite, PiToModule.fromEnd_apply_single_one, fwdDiff_aux.shiftₗ_apply, Representation.asAlgebraHom_of, LinearMap.prodMapAlgHom_apply_apply, End.eigenspace_def, End.one_apply, LinearMap.isNilpotent_iff_charpoly, preReflection_apply, Algebra.toMatrix_lmul', Submodule.isIdempotentElemEquiv_symm_apply_coe, LieAlgebra.ad_apply, LieAlgebra.toEnd_pow_apply_mem, LinearMap.polyCharpolyAux_baseChange, End.mem_iInf_maxGenEigenspace_iff, FGModuleCat.Iso.conj_eq_conj, End.isSemisimple_neg, End.isSemisimple_zero, LieAlgebra.conj_ad_apply, RestrictScalars.lsmul_apply_apply, IsSemisimpleRing.moduleEnd, AlgEquiv.linearEquivConj_mulLeftRight, LinearEquiv.symm_conj_apply, LinearEquiv.conjAlgEquiv_apply_apply, End.finite_spectrum, LinearMap.eventually_isCompl_ker_pow_range_pow, LinearEquiv.conj_conj_symm, End.eventually_disjoint_ker_pow_range_pow, endVecAlgEquivMatrixEnd_apply_apply, End.commute_id_right, LieModule.isRegular_iff_natTrailingDegree_charpoly_eq_rank, algebraMap_end_apply, LinearMap.polyCharpoly_eq_of_basis, IsSemisimpleModule.exists_end_ringEquiv, End.mem_eigenspace_iff, Ideal.constr_basisSpanSingleton, IsSl2Triple.HasPrimitiveVectorWith.lie_f_pow_toEnd_f, End.instSMulCommClass', AEval.mem_mapSubmodule_symm_apply, End.instIsScalarTower, LieModule.toEnd_pow_lie, Representation.norm_ofDistribMulAction_eq, End.HasUnifEigenvector.apply_eq_smul, End.apply_smulCommClass, Basis.end_repr_symm_apply, LieSubmodule.coe_toEnd, LieModule.toEnd_apply_apply, LieModule.commute_toEnd_of_mem_center_right, IsSemisimpleModule.exists_end_algEquiv, Matrix.toLpLinAlgEquiv_apply_apply_ofLp, LinearMap.polyCharpolyAux_coeff_eval, LieModule.toEnd_baseChange, LocalizedModule.mul_by_divBy, End.genEigenspace_zero_nat, SemimoduleCat.Iso.conj_eq_conj, IsBaseChange.map_id_lsmul_eq_lsmul_algebraMap, LinearMap.mem_selfAdjointSubmodule, End.HasUnifEigenvalue.pow, Representation.norm_self_apply, End.eigenspace_div, jacobson_density, Polynomial.span_minpoly_eq_annihilator, End.genEigenrange_nat, LinearMap.eventually_iInf_range_pow_eq, LieModule.isNilpotent_iff_forall, LieModule.isNilpotent_toEnd_sub_algebraMap, lieEquivMatrix'_symm_apply, IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_divisionRing, Projectivization.smul_def, isNilpotent_tensor_residueField_iff, LinearMap.trace_conj', IsSl2Triple.HasPrimitiveVectorWith.lie_e_pow_succ_toEnd_f, Algebra.toMatrix_lsmul, AlgEquiv.moduleEndSelf_apply_apply, IsSl2Triple.HasPrimitiveVectorWith.lie_h_pow_toEnd_f, End.baseChangeHom_apply_apply, Matrix.isRepresentation.toEnd_surjective, End.instSMulCommClass, Matrix.Represents.add, End.IsSemisimple_smul, Finite.toModuleEnd_moduleEnd_surjective, LinearMap.polyCharpoly_map_eq_charpoly, toModuleEnd_apply, End.hasEigenvalue_iff_isRoot, CliffordAlgebra.foldr'Aux_apply_apply, Matrix.Represents.one, LinearEquiv.conj_id, AlgEquiv.moduleEndSelfOp_symm_apply, IsSemisimpleRing.exists_ringEquiv_pi_matrix_end_mulOpposite, End.mem_invtSubmodule_iff_forall_mem_of_mem, LieAlgebra.IsKilling.cartanEquivDual_apply_apply, End.IsSemisimple_smul_iff, End.mem_genEigenspace_one, LieModule.toEnd_eq_zero_iff, LinearMap.charpoly_sub_smul, End.apply_faithfulSMul, LinearEquiv.conjRingEquiv_symm_apply_apply, LinearMap.restrict_smul_one, Algebra.norm_apply, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_end, LieAlgebra.isNilpotent_ad_of_mem_rootSpace, Representation.ofModule_asAlgebraHom_apply_apply, End.isIntegral, AlgebraicGeometry.tilde.isUnit_algebraMap_end_basicOpen, End.mem_maxGenEigenspace, End.genEigenspace_div, Matrix.isRepresentation.eq_toEnd_of_represents, LieModule.traceForm_apply_apply, LieAlgebra.IsKilling.isSemisimple_ad_of_mem_isCartanSubalgebra, Algebra.baseChange_lmul, LieModule.trace_toEnd_genWeightSpaceChain_eq_zero, End.commute_pow_left_of_commute, RootPairing.toPerfPair_conj_reflection, LieModule.maxGenEigenSpace_toEnd_eq_top, AlgEquiv.moduleEndSelf_symm_apply, LinearEquiv.lieConj_symm, LieAlgebra.rank_eq_natTrailingDegree, End.ker_aeval_ring_hom'_unit_polynomial, Algebra.lmul_isUnit_iff, LinearEquiv.charpoly_conj, isStablyFiniteRing_iff_isDedekindFiniteMonoid_moduleEnd, End.genEigenspace_nat, ker_algebraMap_end, endVecAlgEquivMatrixEnd_symm_apply_apply, AlgEquiv.linearEquivConj_mulRight, ModuleCat.Iso.conj_eq_conj, Representation.leftRegular_norm_apply, End.IsSemisimple.minpoly_squarefree, End.lTensorAlgHom_apply_apply, LieAlgebra.ad_lie, End.mem_submonoidCenter_iff, RootPairing.toPerfPair_flip_conj_coreflection, VertexOperator.ncoeff_eq_zero_of_lt_order, LieModule.isNilpotent_iff_forall', IsLocalizedModule.fromLocalizedModule'_mk, End.mem_genEigenspace_nat, LieSubmodule.coe_toEnd_pow, FDRep.Iso.conj_ρ, LieAlgebra.isNilpotent_range_ad_iff, LieModule.mem_genWeightSpaceOf, instIsStablyFiniteRingEndForallOfFinite, End.isUnit_intrinsicStar_iff, End.mulSemiringActionToAlgEquiv_conjAct_surjective, IsSemisimpleModule.exists_end_algEquiv_pi_matrix_divisionRing, IsLocalizedModule.map_units, LieAlgebra.nilpotent_ad_of_nilpotent_algebra, LieModule.instIsFaithfulEnd, Matrix.represents_iff', End.ringEquivEndFinsupp_apply_apply_support, LinearMap.eventually_codisjoint_ker_pow_range_pow, AlgHom.toEnd_apply, Representation.asModuleEquiv_map_smul, LieModule.coe_lcs_range_toEnd_eq, LieModule.toEnd_module_end, LieAlgebra.mem_zeroRootSubalgebra, End.ker_pow_le_ker_pow_finrank, End.apply_isScalarTower, Matrix.Represents.mul, End.natCast_apply, End.mul_apply, End.mem_spectrum_iff_isRoot_charpoly, End.smulLeft_eq, End.ofNat_apply, LieModule.iterate_toEnd_mem_lowerCentralSeries, addMonoidEndRingEquivInt_symm_apply, Algebra.coe_lmul_eq_mul, LinearMap.nilRank_le_natTrailingDegree_charpoly, End.invtSubmodule.zero, LinearEquiv.conjAlgEquiv_surjective, End.hasEigenvalue_iff_mem_spectrum, LinearMap.not_hasEigenvalue_zero_tfae, LieDerivation.coe_ad_apply_eq_ad_apply, fwdDiff_aux.coe_fwdDiffₗ_pow, Algebra.trace_apply, LinearEquiv.map_mem_invtSubmodule_iff, Algebra.FormallyUnramified.comp_sec, LieAlgebra.isNilpotent_iff_forall, LieAlgebra.ad_ker_eq_bot_of_hasTrivialRadical, End.mem_genEigenspace, TensorProduct.AlgebraTensorModule.smul_eq_lsmul_rTensor, LieAlgebra.isNilpotent_ad_of_isNilpotent, End.mem_subsemiringCenter_iff, End.iterate_succ, End.ringEquivEndFinsupp_symm_apply_apply, LinearMap.baseChange_mul, End.HasEigenvector.pow_apply, Matrix.Represents.algebraMap, FGModuleCat.Iso.conj_hom_eq_conj, fwdDiff_aux.coe_fwdDiffₗ, End.genEigenspace_le_smul, LieModule.commute_toEnd_of_mem_center_left, AEval.mem_mapSubmodule_apply, End.ringHomEndFinsupp_surjective, Representation.asAlgebraHom_mem_of_forall_mem, Matrix.toLpLinAlgEquiv_symm_apply, LieAlgebra.ad_ker_eq_self_module_ker, VertexOperator.coeff_eq_ncoeff, End.exists_isNilpotent_isSemisimple, End.HasUnifEigenvalue.mem_spectrum, End.eigenspace_aeval_polynomial_degree_1, Algebra.leftMulMatrix_apply, involutive_preReflection, IsSemisimpleModule.exists_end_ringEquiv_pi_matrix_end, RootPairing.Hom.weightHom_injective, LinearMap.rTensor_mul, LinearMap.trace_map, LinearMap.polyCharpoly_coeff_eval, End.mem_subalgebraCenter_iff, Algebra.lsmul_coe, Representation.self_norm_apply, LinearMap.instIsSimpleModuleEndOfNontrivial, LieModule.Weight.hasEigenvalueAt, AlgHom.mulLeftRightMatrix.comp_inv, LinearMap.exists_monic_and_coeff_mem_pow_and_aeval_eq_zero_of_range_le_smul, End.coe_one, LieModule.rank_le_natTrailingDegree_charpoly_ad, RingEquiv.moduleEndSelfOp_symm_apply, LieSubalgebra.coe_ad, LieModule.toEnd_matrix, LieModule.toEnd_pow_comp_lieHom, LinearMap.trace_lie, IsAzumaya.AlgHom.mulLeftRight_bij, LinearMap.polyCharpolyAux_map_eq_toMatrix_charpoly, End.instNontrivial, LieSubalgebra.ad_comp_incl_eq
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