Theorems · Theorem · functional analysis

OrthonormalBasis.sum_inner_mul_inner

∀ {ι : Type u_1} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι] (b : OrthonormalBasis ι 𝕜 E) (x y : E),
  ∑ i, inner 𝕜 x (b i) * inner 𝕜 (b i) y = inner 𝕜 x y

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

3 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintype