Theorems · Theorem · functional analysis

Orthonormal.orthonormal_of_forall_eq_or_eq_neg

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_4} {v w : ι → E}, Orthonormal 𝕜 v → (∀ (i : ι), w i = v i ∨ w i = -v i) → Orthonormal 𝕜 w

Given an orthonormal family, a second family of vectors is orthonormal if every vector equals the corresponding vector in the original family or its negation.

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

1 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace