`BookProof.ChapterAbelianVonNeumannFinite.abelian_commutant_isomorphic_ellInfty` {A : Matrix n n ℂ} (hA : A.IsHermitian) (hdist : Function.Injective hA.eigenvalues) : ∃ f : (n → ℂ)

Proved

BookProof.ChapterAbelianVonNeumannFinite.abelian_commutant_isomorphic_ellInfty

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterAbelianVonNeumannFinite.

BookProof.ChapterAbelianVonNeumannFinite.abelian_commutant_isomorphic_ellInfty {A : Matrix n n ℂ} (hA : A.IsHermitian) (hdist : Function.Injective hA.eigenvalues) : ∃ f : (n → ℂ) →⋆ₐ[ℂ] Matrix n n ℂ, Function.Injective f ∧ Set.range f = {M : Matrix n n ℂ | M * A = A * M}

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

Preamble

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


open Matrix


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

Formal statement

theorem BookProof.ChapterAbelianVonNeumannFinite.abelian_commutant_isomorphic_ellInfty {A : Matrix n n ℂ} (hA : A.IsHermitian)
    (hdist : Function.Injective hA.eigenvalues) :
    ∃ f : (n → ℂ) →⋆ₐ[ℂ] Matrix n n ℂ,
      Function.Injective f ∧ Set.range f = {M : Matrix n n ℂ | M * A = A * M} := by sorry

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