`BookProof.ChapterA.Rcomplex_realCommutant_eq_complex` (M : System ℂ V) (hSchur : IsSchurFull M) (hNo : NoAntilinearCommutant M) (S : V →L[ℝ] V) : RealCommutes M S ↔ ∃ c : ℂ, S = c

Proved

BookProof.ChapterA.Rcomplex_realCommutant_eq_complex

by leonardopedro · Oct 17, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterA2c.

BookProof.ChapterA.Rcomplex_realCommutant_eq_complex (M : System ℂ V) (hSchur : IsSchurFull M) (hNo : NoAntilinearCommutant M) (S : V →L[ℝ] V) : RealCommutes M S ↔ ∃ c : ℂ, S = cembed c

Formalization note: Lean 4 identifier BookProof.ChapterA.Rcomplex_realCommutant_eq_complex.

Preamble

-- Generated from ChapterA2c.lean — theorem BookProof.ChapterA.Rcomplex_realCommutant_eq_complex
import Mathlib
import Definitions.Def_ChapterA2c
import Definitions.Def_ChapterA
open BookProof.ChapterA
open BookProof.ChapterA


open scoped ComplexConjugate InnerProductSpace Quaternion


variable {V : Type*} [NormedAddCommGroup V] [InnerProductSpace ℂ V] [CompleteSpace V]

Formal statement

theorem BookProof.ChapterA.Rcomplex_realCommutant_eq_complex (M : System ℂ V) (hSchur : IsSchurFull M)
    (hNo : NoAntilinearCommutant M) (S : V →L[ℝ] V) :
    RealCommutes M S ↔ ∃ c : ℂ, S = cembed c := by sorry

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