Theorems · Theorem · linear algebra

Module.End.map_smul_of_iInf_genEigenspace_ne_bot

∀ {R : Type v} {M : Type w} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsDomain R]
  [Module.IsTorsionFree R M] {L : Type u_1} {F : Type u_2} [inst_5 : SMul R L] [inst_6 : FunLike F L (Module.End R M)]
  [MulActionHomClass F R L (Module.End R M)] (f : F) (μ : L → R) (k : ℕ∞),
  ⨅ x, ((f x).genEigenspace (μ x)) k ≠ ⊥ → ∀ (t : R) (x : L), μ (t • x) = t • μ x

Defined in

Mathlib.LinearAlgebra.Eigenspace.Basic

Cited by

0 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleIsDomainModule.IsTorsionFreeSMulFunLikeMulActionHomClass