Theorems · Theorem · functional analysis

Orthonormal.linearIsometryEquiv_symm_apply_single_one

∀ {ι : Type u_1} {𝕜 : Type u_2} [inst : RCLike 𝕜] {E : Type u_3} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : CompleteSpace E] {v : ι → E} (hv : Orthonormal 𝕜 v)
  [inst_4 : DecidableEq ι] (h : ⊤ ≤ (Submodule.span 𝕜 (Set.range v)).topologicalClosure) (i : ι),
  ⋯.linearIsometryEquiv.symm (lp.single 2 i 1) = v i

Defined in

Mathlib.Analysis.InnerProductSpace.l2Space

Cited by

1 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpaceDecidableEq