`BookProof.ChapterA3.adjoint_mgammaLin` (μ : Fin 4) : LinearMap.adjoint (mgammaLin μ) = (if μ = 0 then (-1 : ℂ) else 1) • mgammaLin μ

Proved

BookProof.ChapterA3.adjoint_mgammaLin

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliCommutant.

BookProof.ChapterA3.adjoint_mgammaLin (μ : Fin 4) : LinearMap.adjoint (mgammaLin μ) = (if μ = 0 then (-1 : ℂ) else 1) • mgammaLin μ

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

Preamble

-- Generated from ChapterPauliCommutant.lean — theorem BookProof.ChapterA3.adjoint_mgammaLin
import Mathlib
import Definitions.Def_ChapterPauliCommutant
import Definitions.Def_ChapterA3
open BookProof.ChapterA3


open Matrix

Formal statement

theorem BookProof.ChapterA3.adjoint_mgammaLin (μ : Fin 4) :
    LinearMap.adjoint (mgammaLin μ) = (if μ = 0 then (-1 : ℂ) else 1) • mgammaLin μ := by sorry

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