Theorems · Definition · linear algebra

Module.End.eigenspace

{R : Type v} →
  {M : Type w} →
    [inst : CommRing R] → [inst_1 : AddCommGroup M] → [inst_2 : Module R M] → Module.End R M → R → Submodule R M

The submodule eigenspace f μ for a linear map f and a scalar μ consists of all vectors x such that f x = μ • x. (Def 5.52 of [axler2024]).

Defined in

Mathlib.LinearAlgebra.Eigenspace.Basic

Cited by

56 results in Mathlib

Foundations

Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModule