Theorems · Theorem · functional analysis

OrthonormalBasis.reindex_apply

∀ {ι : Type u_1} {ι' : Type u_2} {𝕜 : Type u_3} [inst : RCLike 𝕜] {E : Type u_4} [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : Fintype ι] [inst_4 : Fintype ι'] (b : OrthonormalBasis ι 𝕜 E) (e : ι ≃ ι')
  (i' : ι'), (b.reindex e) i' = b (e.symm i')

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

3 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeFintype