Theorems · Definition · functional analysis

OrthonormalBasis.equiv

{ι : Type u_1} →
  {ι' : Type u_2} →
    {𝕜 : Type u_3} →
      [inst : RCLike 𝕜] →
        {E : Type u_4} →
          [inst_1 : NormedAddCommGroup E] →
            [inst_2 : InnerProductSpace 𝕜 E] →
              [inst_3 : Fintype ι] →
                {E' : Type u_7} →
                  [inst_4 : Fintype ι'] →
                    [inst_5 : NormedAddCommGroup E'] →
                      [inst_6 : InnerProductSpace 𝕜 E'] →
                        OrthonormalBasis ι 𝕜 E → OrthonormalBasis ι' 𝕜 E' → ι ≃ ι' → E ≃ₗᵢ[𝕜] E'

The LinearIsometryEquiv which maps an orthonormal basis to another. This is a convenience wrapper around Orthonormal.equiv.

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

8 results in Mathlib

Foundations

Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeFintypeNormedAddCommGroupInnerProductSpace