`BookProof.ChapterA3.exists_real_of_conj_fixed` {N : Matrix (Fin 4) (Fin 4) ℂ} (hN : N.map (starRingEnd ℂ) = N) : ∃ M : Matrix (Fin 4) (Fin 4) ℝ, toC M = N

Proved

BookProof.ChapterA3.exists_real_of_conj_fixed

by leonardopedro · Oct 6, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA3b.

BookProof.ChapterA3.exists_real_of_conj_fixed {N : Matrix (Fin 4) (Fin 4) ℂ} (hN : N.map (starRingEnd ℂ) = N) : ∃ M : Matrix (Fin 4) (Fin 4) ℝ, toC M = N

Formalization note: Lean 4 identifier BookProof.ChapterA3.exists_real_of_conj_fixed.

Preamble

-- Generated from ChapterA3b.lean — theorem BookProof.ChapterA3.exists_real_of_conj_fixed
import Mathlib
import Definitions.Def_ChapterA3b
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix
open scoped ComplexConjugate

Formal statement

theorem BookProof.ChapterA3.exists_real_of_conj_fixed {N : Matrix (Fin 4) (Fin 4) ℂ}
    (hN : N.map (starRingEnd ℂ) = N) : ∃ M : Matrix (Fin 4) (Fin 4) ℝ, toC M = N := by sorry

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