Theorems · Theorem · functional analysis

HilbertBasis.hasSum_orthogonalProjectionOnto

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] {U : Submodule 𝕜 E} [inst_3 : CompleteSpace ↥U] (b : HilbertBasis ι 𝕜 ↥U) (x : E),
  HasSum (fun i => inner 𝕜 (↑(b i)) x • b i) (U.orthogonalProjectionOnto x)

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

1 results in Mathlib

Foundations

Depth 236 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace