Theorems · Theorem · linear algebra

Module.Basis.baseChange_repr_tmul

∀ {R : Type u_1} {M : Type u_3} {ι : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  (S : Type u_7) [inst_3 : Semiring S] [inst_4 : Algebra R S] (b : Module.Basis ι R M) (x : S) (y : M) (i : ι),
  ((Module.Basis.baseChange S b).repr (x ⊗ₜ[R] y)) i = (b.repr y) i • x

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

4 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleSemiringAlgebra