Theorems · Definition · linear algebra

Matrix.Represents

{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) → [DecidableEq ι] → Matrix ι ι R → Module.End R M → Prop

We say that a matrix represents an endomorphism of M if the matrix acting on ι → R is equal to f via the projection (ι → R) →ₗ[R] M given by a fixed (spanning) set.

Defined in

Mathlib.LinearAlgebra.Matrix.Charpoly.LinearMap

Cited by

14 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FintypeAddCommGroupCommRingModuleDecidableEq