Theorems · Theorem · linear algebra

Matrix.toLin_apply

∀ {R : Type u_1} [inst : CommSemiring R] {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] (M : Matrix m n R)
  (v : M₁), ((Matrix.toLin v₁ v₂) M) v = ∑ j, M.mulVec (⇑(v₁.repr v)) j • v₂ j

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringFintypeDecidableEqAddCommMonoidAddCommMonoidModuleModuleFintype