{m : ℕ} (w : Fin m → E) (c : EuclideanSpace ℂ (Fin m)) : 0 ≤ (⟪c, gramOp w c⟫_ℂ).re

Proved

BookProof.ChapterSirkGramWhitening.gramOp_nonneg

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

sirkspectral-theorytimepiece

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

Preamble

-- Generated from ChapterSirkGramWhitening.lean — theorem BookProof.ChapterSirkGramWhitening.gramOp_nonneg
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.gramOp_nonneg {m : ℕ} (w : Fin m → E) (c : EuclideanSpace ℂ (Fin m)) :
    0 ≤ (⟪c, gramOp w c⟫_ℂ).re := by sorry

Source

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

View graph