{d : ℕ} {v : Fin d → E} (hv : Orthonormal ℂ v) : (adjoint (synthesis v)).comp (synthesis v) = ContinuousLinearMap.id ℂ (EuclideanSpace ℂ (Fin d))

-- Generated from ChapterSirkGramCutoff.lean — theorem BookProof.ChapterSirkGramCutoff.synthesis_isometry_of_orthonormal
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.synthesis_isometry_of_orthonormal {d : ℕ} {v : Fin d → E} (hv : Orthonormal ℂ v) :
    (adjoint (synthesis v)).comp (synthesis v)
      = ContinuousLinearMap.id ℂ (EuclideanSpace ℂ (Fin d)) := by sorry