Theorems · Theorem · functional analysis

Orthonormal.orthogonalFamily

∀ {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 : ι → E} (hv : Orthonormal 𝕜 v),
  OrthogonalFamily 𝕜 (fun _i => 𝕜) fun i => LinearIsometry.toSpanSingleton 𝕜 E ⋯

Defined in

Mathlib.Analysis.InnerProductSpace.Subspace

Cited by

1 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpace