Theorems · Theorem · linear algebra

LinearMap.toMatrixAlgEquiv_transpose_apply

∀ {R : Type u_1} [inst : CommSemiring R] {n : Type u_4} [inst_1 : Fintype n] [inst_2 : DecidableEq n] {M₁ : Type u_5}
  [inst_3 : AddCommMonoid M₁] [inst_4 : Module R M₁] (v₁ : Module.Basis n R M₁) (f : M₁ →ₗ[R] M₁) (j : n),
  ((LinearMap.toMatrixAlgEquiv v₁) f).transpose j = ⇑(v₁.repr (f (v₁ j)))

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

1 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringFintypeDecidableEqAddCommMonoidModule