Theorems · Theorem · linear algebra

Module.Basis.linearCombination_dualBasis

∀ {R : Type uR} {M : Type uM} {ι : Type uι} [inst : CommSemiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M]
  [inst_3 : DecidableEq ι] (b : Module.Basis ι R M) [inst_4 : Finite ι] (f : ι →₀ R) (i : ι),
  ((Finsupp.linearCombination R ⇑b.dualBasis) f) (b i) = f i

Defined in

Mathlib.LinearAlgebra.Dual.Basis

Cited by

2 results in Mathlib

Foundations

Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleDecidableEqFinite