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

Proved

BookProof.ChapterSirkGramCutoff.exists_gramEigen

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

sirkspectral-theorytimepiece

Lean 4 theorem BookProof.ChapterSirkGramCutoff.exists_gramEigen (module BookProof.ChapterSirkGramCutoff), source chapter BookProof/ChapterChapterSirkGramCutoff.lean.

Preamble

-- Generated from ChapterSirkGramCutoff.lean — theorem BookProof.ChapterSirkGramCutoff.exists_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]

Formal statement

theorem BookProof.ChapterSirkGramCutoff.exists_gramEigen {m : ℕ} (w : Fin m → E) :
    ∃ (u : OrthonormalBasis (Fin m) ℂ (EuclideanSpace ℂ (Fin m))) (lam : Fin m → ℝ),
      IsGramEigen w u lam := by sorry

Source

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

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