`BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec` {A : E →L[ℂ] E} {w : ℂ} {n : ℕ} (hn : 0 < n) (hw : IsPrimitiveRoot w n) (z : ℂ) (y : E) : ∑ k ∈ Finset.range n, pearcyVec A

Proved

BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterNumericalRangeCrouzeix.

BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec {A : E →L[ℂ] E} {w : ℂ} {n : ℕ} (hn : 0 < n) (hw : IsPrimitiveRoot w n) (z : ℂ) (y : E) : ∑ k ∈ Finset.range n, pearcyVec A (w ^ k * z) n y = (n : ℂ) • y

Formalization note: Lean 4 identifier BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec.

Preamble

-- Generated from ChapterNumericalRangeCrouzeix.lean — theorem BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec
import Mathlib
import Definitions.Def_ChapterNumericalRangeCrouzeix
open BookProof.ChapterNumericalRangeCrouzeix


open scoped InnerProductSpace


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

Formal statement

theorem BookProof.ChapterNumericalRangeCrouzeix.sum_pearcyVec {A : E →L[ℂ] E} {w : ℂ} {n : ℕ} (hn : 0 < n)
    (hw : IsPrimitiveRoot w n) (z : ℂ) (y : E) :
    ∑ k ∈ Finset.range n, pearcyVec A (w ^ k * z) n y = (n : ℂ) • y := by sorry

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