Theorems · Theorem · linear algebra

Module.End.mem_genEigenspace

∀ {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}, x ∈ (f.genEigenspace μ) k ↔ ∃ l, ↑l ≤ k ∧ x ∈ ((f - μ • 1) ^ l).ker

Defined in

Mathlib.LinearAlgebra.Eigenspace.Basic

Cited by

4 results in Mathlib

Foundations

Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule