Theorems · Theorem · functional analysis

InnerProductSpace.gramSchmidt_def

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_3} [inst_3 : LinearOrder ι] [inst_4 : LocallyFiniteOrderBot ι] [inst_5 : WellFoundedLT ι] (f : ι → E)
  (n : ι),
  InnerProductSpace.gramSchmidt 𝕜 f n = f n - ∑ i < n, (𝕜 ∙ InnerProductSpace.gramSchmidt 𝕜 f i).starProjection (f n)

This lemma uses ∑ i in instead of ∑ i :.

Defined in

Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho

Cited by

5 results in Mathlib

Foundations

Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceLinearOrderLocallyFiniteOrderBotWellFoundedLT