Theorems · Theorem · linear algebra
Module.End.HasUnifEigenvector.hasUnifEigenvalue
∀ {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∞} {x : M}, f.HasUnifEigenvector μ k x → f.HasUnifEigenvalue μ k- Defined in
- Mathlib.LinearAlgebra.Eigenspace.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 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.
Cites10
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
- ENatstatement and proof · cited by 4,985
- Module.Endstatement and proof · cited by 774
- Module.End.genEigenspaceproof · cited by 70
- Submodule.ne_bot_iffproof · cited by 28
- Module.End.HasUnifEigenvaluestatement · cited by 18
- Module.End.HasUnifEigenvectorstatement and proof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- Module.End.hasEigenvalue_of_hasEigenvectorproof · cited by 8