Theorems · Theorem · linear algebra

Module.Basis.tensorProduct_apply

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} {N : Type u_4} {ι : Type u_5} {κ : Type u_6} [inst : CommSemiring R]
  [inst_1 : Semiring S] [inst_2 : Algebra R S] [inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M]
  [inst_6 : IsScalarTower R S M] [inst_7 : AddCommMonoid N] [inst_8 : Module R N] (b : Module.Basis ι S M)
  (c : Module.Basis κ R N) (i : ι) (j : κ), (b.tensorProduct c) (i, j) = b i ⊗ₜ[R] c j

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

9 results in Mathlib

Foundations

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

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModuleModuleIsScalarTowerAddCommMonoidModule