Theorems · Theorem · linear algebra
Module.End.HasUnifEigenvalue.isNilpotent_of_isNilpotent
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsDomain R]
[Module.IsTorsionFree R M] {f : Module.End R M}, IsNilpotent f → ∀ {μ : R}, f.HasUnifEigenvalue μ 1 → IsNilpotent μA nilpotent endomorphism has nilpotent eigenvalues.
See also LinearMap.isNilpotent_trace_of_isNilpotent.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- RingHom.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- ENatstatement · cited by 4,985
- IsDomainstatement and proof · cited by 2,196
- Module.Endstatement and proof · cited by 774
- Module.IsTorsionFreestatement and proof · cited by 600
- IsNilpotentstatement and proof · cited by 248
- Module.End.HasUnifEigenvaluestatement and proof · cited by 18
- Module.End.HasUnifEigenvectorproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.HasEigenvalue.isNilpotent_of_isNilpotentproof · cited by 1