Theorems · Theorem · linear algebra

PiTensorProduct.dualDistribInvOfBasis_apply

∀ {ι : Type u_1} {R : Type u_2} {κ : ι → Type u_3} {M : ι → Type u_4} [inst : CommRing R]
  [inst_1 : (i : ι) → AddCommGroup (M i)] [inst_2 : (i : ι) → Module R (M i)] [inst_3 : Fintype ι]
  [inst_4 : (i : ι) → Fintype (κ i)] (b : (i : ι) → Module.Basis (κ i) R (M i))
  (f : Module.Dual R (PiTensorProduct R fun i => M i)),
  (PiTensorProduct.dualDistribInvOfBasis b) f =
    ∑ p, f (⨂ₜ[R] (i : ι), (b i) (p i)) • (PiTensorProduct.tprod R) fun i => (b i).dualBasis (p i)

Defined in

Mathlib.LinearAlgebra.PiTensorProduct.Dual

Cited by

2 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleFintypeFintype