Theorems · Theorem · linear algebra

TensorProduct.dualDistribInvOfBasis_apply

∀ {R : Type u_7} {M : Type u_8} {N : Type u_9} {ι : Type u_10} {κ : Type u_11} [inst : DecidableEq ι]
  [inst_1 : DecidableEq κ] [inst_2 : Fintype ι] [inst_3 : Fintype κ] [inst_4 : CommSemiring R]
  [inst_5 : AddCommMonoid M] [inst_6 : AddCommMonoid N] [inst_7 : Module R M] [inst_8 : Module R N]
  (b : Module.Basis ι R M) (c : Module.Basis κ R N) (f : Module.Dual R (TensorProduct R M N)),
  (TensorProduct.dualDistribInvOfBasis b c) f = ∑ i, ∑ j, f (b i ⊗ₜ[R] c j) • b.dualBasis i ⊗ₜ[R] c.dualBasis j

Defined in

Mathlib.LinearAlgebra.Contraction

Cited by

3 results in Mathlib

Foundations

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

Assumes

DecidableEqDecidableEqFintypeFintypeCommSemiringAddCommMonoidAddCommMonoidModuleModule