Theorems · Definition · functional analysis

OrthonormalBasis.map

{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] →
              {G : Type u_7} →
                [inst_4 : NormedAddCommGroup G] →
                  [inst_5 : InnerProductSpace 𝕜 G] → OrthonormalBasis ι 𝕜 E → (E ≃ₗᵢ[𝕜] G) → OrthonormalBasis ι 𝕜 G

Mapping an orthonormal basis along a LinearIsometryEquiv.

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

10 results in Mathlib

Foundations

Depth 222 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeNormedAddCommGroupInnerProductSpace