Theorems · Theorem · linear algebra

TensorProduct.equivFinsuppOfBasisLeft_symm

∀ {R : Type u_1} {M : Type u_3} {N : Type u_4} {ι : Type u_5} [inst : CommSemiring R] [inst_1 : AddCommMonoid M]
  [inst_2 : Module R M] [inst_3 : AddCommMonoid N] [inst_4 : Module R N] [inst_5 : DecidableEq ι]
  (ℬ : Module.Basis ι R M),
  ↑(TensorProduct.equivFinsuppOfBasisLeft ℬ).symm = (Finsupp.lsum R) fun i => (TensorProduct.mk R M N) (ℬ i)

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

2 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModuleDecidableEq