Theorems · Definition · functional analysis

Module.Basis.toOrthonormalBasis

{ι : Type u_1} →
  {𝕜 : Type u_3} →
    [inst : RCLike 𝕜] →
      {E : Type u_4} →
        [inst_1 : NormedAddCommGroup E] →
          [inst_2 : InnerProductSpace 𝕜 E] →
            [inst_3 : Fintype ι] → (v : Module.Basis ι 𝕜 E) → Orthonormal 𝕜 ⇑v → OrthonormalBasis ι 𝕜 E

A basis that is orthonormal is an orthonormal basis.

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

5 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintype