Theorems · Theorem · functional analysis

InnerProductSpace.gramSchmidt_ne_zero_coe

∀ {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), LinearIndependent 𝕜 (f ∘ Subtype.val) → InnerProductSpace.gramSchmidt 𝕜 f n ≠ 0

Defined in

Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho

Cited by

2 results in Mathlib

Foundations

Depth 189 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceLinearOrderLocallyFiniteOrderBotWellFoundedLT