Theorems · Definition · functional analysis

Orthonormal.equiv

{𝕜 : Type u_1} →
  {E : Type u_2} →
    [inst : RCLike 𝕜] →
      [inst_1 : SeminormedAddCommGroup E] →
        [inst_2 : InnerProductSpace 𝕜 E] →
          {ι : Type u_4} →
            {ι' : Type u_5} →
              {E' : Type u_7} →
                [inst_3 : SeminormedAddCommGroup E'] →
                  [inst_4 : InnerProductSpace 𝕜 E'] →
                    {v : Module.Basis ι 𝕜 E} →
                      Orthonormal 𝕜 ⇑v → {v' : Module.Basis ι' 𝕜 E'} → Orthonormal 𝕜 ⇑v' → ι ≃ ι' → E ≃ₗᵢ[𝕜] E'

A linear isometric equivalence that sends an orthonormal basis to a given orthonormal basis.

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

7 results in Mathlib

Foundations

Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace