Theorems · Theorem · linear algebra

Algebra.leftMulMatrix_mulVec_repr

∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : Semiring S] [inst_2 : Algebra R S] {m : Type u_3}
  [inst_3 : Fintype m] [inst_4 : DecidableEq m] (b : Module.Basis m R S) (x y : S),
  ((Algebra.leftMulMatrix b) x).mulVec ⇑(b.repr y) = ⇑(b.repr (x * y))

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

2 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraFintypeDecidableEq