`BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal` {A : Matrix n n ℂ} (hA : A.IsHermitian) (hdist : Function.Injective hA.eigenvalues) : {M : Matrix n n ℂ |

Proved

BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianVonNeumannFinite.

BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal {A : Matrix n n ℂ} (hA : A.IsHermitian) (hdist : Function.Injective hA.eigenvalues) : {M : Matrix n n ℂ | M * A = A * M} = Set.range (conjDiagonal hA.eigenvectorUnitary)

Formalization note: Lean 4 identifier BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal.

Preamble

-- Generated from ChapterAbelianVonNeumannFinite.lean — theorem BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal
import Mathlib
import Definitions.Def_ChapterAbelianVonNeumannFinite
open BookProof.ChapterAbelianVonNeumannFinite


open Matrix


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

Formal statement

theorem BookProof.ChapterAbelianVonNeumannFinite.commutant_eq_range_conjDiagonal {A : Matrix n n ℂ} (hA : A.IsHermitian)
    (hdist : Function.Injective hA.eigenvalues) :
    {M : Matrix n n ℂ | M * A = A * M} = Set.range (conjDiagonal hA.eigenvectorUnitary) := by sorry

View graph