Theorems · Theorem · functional analysis

InnerProductSpace.gramSchmidtOrthonormalBasis_apply

∀ {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]
  [inst_6 : Fintype ι] [inst_7 : FiniteDimensional 𝕜 E] (h : Module.finrank 𝕜 E = Fintype.card ι) {f : ι → E} {i : ι},
  InnerProductSpace.gramSchmidtNormed 𝕜 f i ≠ 0 →
    (InnerProductSpace.gramSchmidtOrthonormalBasis h f) i = InnerProductSpace.gramSchmidtNormed 𝕜 f i

Defined in

Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho

Cited by

3 results in Mathlib

Foundations

Depth 237 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceLinearOrderLocallyFiniteOrderBotWellFoundedLTFintypeFiniteDimensional