Theorems · Definition · functional analysis

OrthonormalBasis.mulOpposite

{𝕜 : Type u_1} →
  [inst : RCLike 𝕜] →
    {ι : Type u_3} →
      {H : Type u_4} →
        [inst_1 : NormedAddCommGroup H] →
          [inst_2 : InnerProductSpace 𝕜 H] → [inst_3 : Fintype ι] → OrthonormalBasis ι 𝕜 H → OrthonormalBasis ι 𝕜 Hᵐᵒᵖ

The multiplicative opposite of an orthonormal basis b, i.e., b i ↦ op (b i).

Defined in

Mathlib.Analysis.InnerProductSpace.MulOpposite

Cited by

1 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintype