Theorems · Theorem · linear algebra
Module.End.genEigenspace_top_eq_maxUnifEigenspaceIndex
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsNoetherian R M]
(f : Module.End R M) (μ : R), (f.genEigenspace μ) ⊤ = (f.genEigenspace μ) ↑(f.maxUnifEigenspaceIndex μ)For an endomorphism of a Noetherian module, the maximal eigenspace is always of the form kernel
(f - μ • id) ^ k for some k.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setproof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement and proof · cited by 7,192
- ENatstatement and proof · cited by 4,985
- Set.rangeproof · cited by 4,705
- iSupproof · cited by 2,415
- Set.extproof · cited by 2,266
- le_reflproof · cited by 2,061
Cited by5
Results whose statement or proof uses this declaration.
- Module.End.maxGenEigenspace_eqproof · cited by 3
- Module.End.genEigenspace_le_genEigenspace_finrankproof · cited by 2
- Module.End.genEigenspace_le_genEigenspace_maxUnifEigenspaceIndexproof · cited by 1
- Module.End.isNilpotent_restrict_genEigenspace_topproof · cited by 0
- Module.End.maxGenEigenspace_eq_genEigenspace_finrankproof · cited by 0