(heig : IsGramEigen w u lam) (k : Fin m) : ‖synthesis w (u k)‖ ^ 2 = lam k

-- Generated from ChapterSirkGramCutoff.lean — theorem BookProof.ChapterSirkGramCutoff.norm_sq_synthesis_gramEigen
import Mathlib
import Definitions.Def_ChapterSirkGramCutoff
open BookProof.ChapterSirkGramCutoff









noncomputable section


open scoped InnerProductSpace
open BookProof.ChapterSirkGramWhitening
open ContinuousLinearMap

variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] [CompleteSpace E]






variable {m : ℕ} {w : Fin m → E}
variable {u : OrthonormalBasis (Fin m) ℂ (EuclideanSpace ℂ (Fin m))} {lam : Fin m → ℝ}

theorem BookProof.ChapterSirkGramCutoff.norm_sq_synthesis_gramEigen (heig : IsGramEigen w u lam) (k : Fin m) :
    ‖synthesis w (u k)‖ ^ 2 = lam k := by sorry