Theorems · Theorem · functional analysis

Orthonormal.equiv_apply

∀ {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'] {ι' : Type u_9}
  {v : Module.Basis ι 𝕜 E} (hv : Orthonormal 𝕜 ⇑v) {v' : Module.Basis ι' 𝕜 E'} (hv' : Orthonormal 𝕜 ⇑v') (e : ι ≃ ι')
  (i : ι), (hv.equiv hv' e) (v i) = v' (e i)

Defined in

Mathlib.Analysis.InnerProductSpace.Orthonormal

Cited by

3 results in Mathlib

Foundations

Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeSeminormedAddCommGroupInnerProductSpaceSeminormedAddCommGroupInnerProductSpace