Theorems · Theorem · functional analysis

LinearEquiv.isometryOfOrthonormal_toLinearEquiv

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : SeminormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {ι : Type u_4} {E' : Type u_7} [inst_3 : SeminormedAddCommGroup E'] [inst_4 : InnerProductSpace 𝕜 E'] (f : E ≃ₗ[𝕜] E')
  {v : Module.Basis ι 𝕜 E} (hv : Orthonormal 𝕜 ⇑v) (hf : Orthonormal 𝕜 (⇑f ∘ ⇑v)),
  (f.isometryOfOrthonormal hv hf).toLinearEquiv = f

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

0 results in Mathlib

Foundations

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

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace