Theorems · Theorem · linear algebra

Submodule.inf_iSup_genEigenspace

∀ {K : Type u_1} {V : Type u_2} [inst : Field K] [inst_1 : AddCommGroup V] [inst_2 : Module K V] {p : Submodule K V}
  {f : Module.End K V} [FiniteDimensional K V],
  (∀ x ∈ p, f x ∈ p) → ∀ (k : ℕ∞), p ⊓ ⨆ μ, (f.genEigenspace μ) k = ⨆ μ, p ⊓ (f.genEigenspace μ) k

Defined in

Mathlib.LinearAlgebra.Eigenspace.Triangularizable

Cited by

1 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldAddCommGroupModuleFiniteDimensional