`BookProof.AbelianDiagonal.mem_commutant_of_diagonal` (e : n → ℂ) (d : n → ℂ) : Matrix.diagonal e * Matrix.diagonal d = Matrix.diagonal d * Matrix.diagonal e

Proved

BookProof.AbelianDiagonal.mem_commutant_of_diagonal

by leonardopedro · Oct 7, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonal.

BookProof.AbelianDiagonal.mem_commutant_of_diagonal (e : n → ℂ) (d : n → ℂ) : Matrix.diagonal e * Matrix.diagonal d = Matrix.diagonal d * Matrix.diagonal e

Formalization note: Lean 4 identifier BookProof.AbelianDiagonal.mem_commutant_of_diagonal.

Preamble

-- Generated from ChapterAbelianDiagonal.lean — theorem BookProof.AbelianDiagonal.mem_commutant_of_diagonal
import Mathlib
import Definitions.Def_ChapterAbelianDiagonal
open BookProof.AbelianDiagonal



open Matrix

variable {n : Type*} [Fintype n] [DecidableEq n]

Formal statement

theorem BookProof.AbelianDiagonal.mem_commutant_of_diagonal (e : n → ℂ) (d : n → ℂ) :
    Matrix.diagonal e * Matrix.diagonal d = Matrix.diagonal d * Matrix.diagonal e := by sorry

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