Theorems · Theorem · linear algebra

Matrix.toLin_mul_apply

∀ {R : Type u_1} [inst : CommSemiring R] {l : Type u_2} {m : Type u_3} {n : Type u_4} [inst_1 : Fintype n]
  [inst_2 : DecidableEq n] {M₁ : Type u_5} {M₂ : Type u_6} [inst_3 : AddCommMonoid M₁] [inst_4 : AddCommMonoid M₂]
  [inst_5 : Module R M₁] [inst_6 : Module R M₂] (v₁ : Module.Basis n R M₁) (v₂ : Module.Basis m R M₂)
  [inst_7 : Fintype m] {M₃ : Type u_7} [inst_8 : AddCommMonoid M₃] [inst_9 : Module R M₃] (v₃ : Module.Basis l R M₃)
  [inst_10 : Finite l] [inst_11 : DecidableEq m] (A : Matrix l m R) (B : Matrix m n R) (x : M₁),
  ((Matrix.toLin v₁ v₃) (A * B)) x = ((Matrix.toLin v₂ v₃) A) (((Matrix.toLin v₁ v₂) B) x)

Shortcut lemma for Matrix.toLin_mul and LinearMap.comp_apply.

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringFintypeDecidableEqAddCommMonoidAddCommMonoidModuleModuleFintypeAddCommMonoidModuleFiniteDecidableEq