Theorems · Theorem · linear algebra

LinearMap.restrictScalars_toMatrix

∀ {R : Type u_1} [inst : CommSemiring R] {m : Type u_3} [inst_1 : Fintype m] [inst_2 : DecidableEq m] {A : Type u_4}
  {M : Type u_5} {n : Type u_6} [inst_3 : Fintype n] [inst_4 : DecidableEq n] [inst_5 : CommSemiring A]
  [inst_6 : AddCommMonoid M] [inst_7 : Module R M] [inst_8 : Module A M] [inst_9 : Algebra R A]
  [inst_10 : IsScalarTower R A M] (bA : Module.Basis m R A) (bM : Module.Basis n A M) (f : M →ₗ[A] M),
  (LinearMap.toMatrix (bA.smulTower' bM) (bA.smulTower' bM)) (↑R f) =
    (Matrix.comp n n m m R) (((LinearMap.toMatrix bM bM) f).map ⇑(Algebra.leftMulMatrix bA))

Defined in

Mathlib.LinearAlgebra.Matrix.ToLin

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommSemiringFintypeDecidableEqFintypeDecidableEqCommSemiringAddCommMonoidModuleModuleAlgebraIsScalarTower