Theorems · Theorem · linear algebra

Module.Basis.toMatrix_smul

∀ {ι : Type u_1} {R₁ : Type u_9} {S : Type u_10} [inst : CommSemiring R₁] [inst_1 : Semiring S] [inst_2 : Algebra R₁ S]
  [inst_3 : Fintype ι] [inst_4 : DecidableEq ι] (x : S) (b : Module.Basis ι R₁ S) (w : ι → S),
  b.toMatrix (x • w) = (Algebra.leftMulMatrix b) x * b.toMatrix w

Defined in

Mathlib.LinearAlgebra.Matrix.Basis

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraFintypeDecidableEq