`BookProof.AbelianDiagonal.commutant_diagonal_eq_diagonal` (M : Matrix n n ℂ) (h : ∀ d : n → ℂ, M * Matrix.diagonal d = Matrix.diagonal d * M) : M = Matrix.diagonal (fun i => M i i

Proved

BookProof.AbelianDiagonal.commutant_diagonal_eq_diagonal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianDiagonal.

BookProof.AbelianDiagonal.commutant_diagonal_eq_diagonal (M : Matrix n n ℂ) (h : ∀ d : n → ℂ, M * Matrix.diagonal d = Matrix.diagonal d * M) : M = Matrix.diagonal (fun i => M i i)

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

Preamble

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



open Matrix

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

Formal statement

theorem BookProof.AbelianDiagonal.commutant_diagonal_eq_diagonal (M : Matrix n n ℂ)
    (h : ∀ d : n → ℂ, M * Matrix.diagonal d = Matrix.diagonal d * M) :
    M = Matrix.diagonal (fun i => M i i) := by sorry

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