Theorems · Theorem · functional analysis

OrthonormalBasis.coe_ofRepr

∀ {ι : Type u_1} {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 : DecidableEq ι] (e : E ≃ₗᵢ[𝕜] EuclideanSpace 𝕜 ι),
  ⇑{ repr := e } = fun i => e.symm (EuclideanSpace.single i 1)

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

2 results in Mathlib

Foundations

Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeDecidableEq