Theorems · Theorem · functional analysis

OrthonormalBasis.sum_sq_inner_right

∀ {ι : Type u_1} [inst : Fintype ι] {E : Type u_7} [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace ℝ E]
  (b : OrthonormalBasis ι ℝ E) (x : E), ∑ i, inner ℝ (b i) x ^ 2 = ‖x‖ ^ 2

Defined in

Mathlib.Analysis.InnerProductSpace.PiL2

Cited by

2 results in Mathlib

Foundations

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

Assumes

FintypeNormedAddCommGroupInnerProductSpace