Theorems · Theorem · linear algebra

LinearMap.toMatrix_mulVec_repr

∀ {R : Type u_1} [inst : CommSemiring R] {m : Type u_3} {n : Type u_4} [inst_1 : Fintype n] [inst_2 : Finite m]
  [inst_3 : DecidableEq n] {M₁ : Type u_5} {M₂ : Type u_6} [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂]
  [inst_6 : Module R M₁] [inst_7 : Module R M₂] (v₁ : Module.Basis n R M₁) (v₂ : Module.Basis m R M₂) (f : M₁ →ₗ[R] M₂)
  (x : M₁), ((LinearMap.toMatrix v₁ v₂) f).mulVec ⇑(v₁.repr x) = ⇑(v₂.repr (f x))

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

5 results in Mathlib

Foundations

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

Assumes

CommSemiringFintypeFiniteDecidableEqAddCommMonoidAddCommMonoidModuleModule