Theorems · Theorem · linear algebra

Module.End.aeval_apply_of_mem_apply_eq_smul

∀ {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} {x : M} {p : Polynomial R}, f x = μ • x → ((Polynomial.aeval f) p) x = Polynomial.eval μ p • x

A variant of Module.End.aeval_apply_of_hasEigenvector which does not require x ≠ 0.

Defined in

Mathlib.LinearAlgebra.Eigenspace.Minpoly

Cited by

0 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule