Theorems · Theorem · functional analysis

FiniteDimensional.orthonormalBasisSingleton_repr_apply

∀ {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 : Unique ι] (h : Module.finrank 𝕜 E = 1) {v : E}
  (hv : ‖v‖ = 1) (w : E),
  (FiniteDimensional.orthonormalBasisSingleton ι 𝕜 h v hv).repr w = EuclideanSpace.single default (inner 𝕜 v w)

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

0 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceFintypeUnique