Theorems · Theorem · linear algebra

Basis.piTensorProduct_repr_tprod_apply

∀ {ι : Type u_1} {R : Type u_2} {M : ι → Type u_3} {κ : ι → Type u_4} [inst : CommSemiring R]
  [inst_1 : (i : ι) → AddCommMonoid (M i)] [inst_2 : (i : ι) → Module R (M i)] [inst_3 : Fintype ι]
  (b : (i : ι) → Module.Basis (κ i) R (M i)) (x : (i : ι) → M i) (p : (i : ι) → κ i),
  ((Basis.piTensorProduct b).repr ((PiTensorProduct.tprod R) x)) p = ∏ i, ((b i).repr (x i)) (p i)

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Basis

Cited by

3 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidModuleFintype