Theorems · Theorem · linear algebra
Module.End.hasUnifEigenvalue_iff_hasUnifEigenvalue_one
∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] {f : Module.End R M}
{μ : R} {k : ℕ∞}, 0 < k → (f.HasUnifEigenvalue μ k ↔ f.HasUnifEigenvalue μ 1)Generalized eigenvalues are actually just eigenvalues.
- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingAddCommGroupModule
Around this declaration
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.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- ENatstatement and proof · cited by 4,985
- Module.Endstatement and proof · cited by 774
- zero_lt_oneproof · cited by 598
- Module.End.HasUnifEigenvaluestatement · cited by 18
- Module.End.HasUnifEigenvalue.ltproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- LieModule.IsTriangularizable.exists_hasEigenvalueproof · cited by 1