Theorems · Theorem · functional analysis

Orthonormal.comp_linearIsometryEquiv

∀ {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'] {v : ι → E},
  Orthonormal 𝕜 v → ∀ (f : E ≃ₗᵢ[𝕜] E'), Orthonormal 𝕜 (⇑f ∘ v)

A linear isometric equivalence preserves the property of being orthonormal.

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

1 results in Mathlib

Foundations

Depth 173 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace