Theorems · Definition · linear algebra

Module.End.maxGenEigenspace

{R : Type v} →
  {M : Type w} →
    [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Module.End R M → R → Submodule R M

The union of the kernels of (f - μ • id) ^ k over all k.

Defined in: Mathlib.LinearAlgebra.Eigenspace.Basic
Cited by: 41 results in Mathlib
Foundations: Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing AddCommGroup Module

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Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coeproof · cited by 62,936
Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
AddCommGroupstatement and proof · cited by 12,871
Top.topproof · cited by 9,680
Submodulestatement · cited by 7,192
Module.Endstatement and proof · cited by 774
Module.End.genEigenspaceproof · cited by 70

Cited by45

Results whose statement or proof uses this declaration.

LieModule.genWeightSpaceOfproof · cited by 17
LieSubalgebra.engelproof · cited by 13
LieAlgebra.IsKilling.lie_eq_smul_of_mem_rootSpaceproof · cited by 8
LieModule.IsTriangularizable.maxGenEigenspace_eq_topstatement · cited by 5
Module.End.IsFinitelySemisimple.maxGenEigenspace_eq_eigenspacestatement · cited by 4
Module.End.mapsTo_maxGenEigenspace_of_commstatement · cited by 3
Module.End.maxGenEigenspace_eqstatement · cited by 3
Module.End.mem_maxGenEigenspacestatement · cited by 2
Module.End.iSup_iInf_maxGenEigenspace_eq_top_of_forall_mapsTostatement and proof · cited by 2
LinearMap.finrank_maxGenEigenspace_zero_eqstatement and proof · cited by 2
Module.End.disjoint_iInf_maxGenEigenspacestatement and proof · cited by 2
LieModule.exists_genWeightSpace_le_ker_of_isNoetherianproof · cited by 2