Theorems · Theorem · functional analysis

InnerProductSpace.gramSchmidt_orthogonal

∀ (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)
  {a b : ι}, a ≠ b → inner 𝕜 (InnerProductSpace.gramSchmidt 𝕜 f a) (InnerProductSpace.gramSchmidt 𝕜 f b) = 0

Gram-Schmidt Orthogonalisation: gramSchmidt produces an orthogonal system of vectors.

Defined in

Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho

Cited by

6 results in Mathlib

Foundations

Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceLinearOrderLocallyFiniteOrderBotWellFoundedLT