Theorems · Theorem · linear algebra

toMatrix_distrib_mul_action_toLinearMap

∀ {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) (x : R),
  (LinearMap.toMatrix v₁ v₁) (DistribSMul.toLinearMap R M₁ x) = Matrix.diagonal fun x_1 => x

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringFintypeDecidableEqAddCommMonoidModule