Theorems · Definition · linear algebra

PiToModule.fromEnd

{ι : Type u_1} →
  [Fintype ι] →
    {M : Type u_2} →
      [inst : AddCommGroup M] →
        (R : Type u_3) → [inst_1 : CommRing R] → [inst_2 : Module R M] → (ι → M) → Module.End R M →ₗ[R] (ι → R) →ₗ[R] M

The endomorphisms of M acts on (ι → R) →ₗ[R] M, and takes the projection to a (ι → R) →ₗ[R] M.

Defined in

Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap

Cited by

9 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeAddCommGroupCommRingModule