{m : ℕ} {w : Fin m → E} (hw : Orthonormal ℂ w) : IsWhitening w (Matrix.toEuclideanCLM (𝕜

Proved

BookProof.ChapterSirkGramWhitening.isWhitening_one_of_orthonormal

by leonardopedro · Sep 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

sirkspectral-theorytimepiece

Lean 4 theorem BookProof.ChapterSirkGramWhitening.isWhitening_one_of_orthonormal (module BookProof.ChapterSirkGramWhitening), source chapter BookProof/ChapterChapterSirkGramWhitening.lean.

Preamble

-- Generated from ChapterSirkGramWhitening.lean — theorem BookProof.ChapterSirkGramWhitening.isWhitening_one_of_orthonormal
import Mathlib
import Definitions.Def_ChapterSirkGramWhitening
open BookProof.ChapterSirkGramWhitening








noncomputable section


open scoped InnerProductSpace
open Matrix
open BookProof.ChapterH4 BookProof.ChapterSirkWhitening

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

Formal statement

theorem BookProof.ChapterSirkGramWhitening.isWhitening_one_of_orthonormal {m : ℕ} {w : Fin m → E} (hw : Orthonormal ℂ w) :
    IsWhitening w (Matrix.toEuclideanCLM (𝕜 := ℂ) (1 : Matrix (Fin m) (Fin m) ℂ)) := by sorry

Source

https://github.com/leonardopedrio/timepiece/blob/61595bc/BookProof/ChapterChapterSirkGramWhitening.lean

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