`BookProof.ChapterPauliSU2.spinorAction_isHermitian` (T : Matrix (Fin 2) (Fin 2) ℂ) {X : Matrix (Fin 2) (Fin 2) ℂ} (hX : Xᴴ = X) : (spinorAction T X)ᴴ = spinorAction T X

Proved

BookProof.ChapterPauliSU2.spinorAction_isHermitian

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterPauliSU2.

BookProof.ChapterPauliSU2.spinorAction_isHermitian (T : Matrix (Fin 2) (Fin 2) ℂ) {X : Matrix (Fin 2) (Fin 2) ℂ} (hX : Xᴴ = X) : (spinorAction T X)ᴴ = spinorAction T X

Formalization note: Lean 4 identifier BookProof.ChapterPauliSU2.spinorAction_isHermitian.

Preamble

-- Generated from ChapterPauliSU2.lean — theorem BookProof.ChapterPauliSU2.spinorAction_isHermitian
import Definitions.Def_ChapterPauliLorentz
import Mathlib
import Definitions.Def_ChapterPauliSU2
open BookProof.ChapterPauliSU2


open Matrix
open scoped BigOperators


open BookProof.ChapterPauliLorentz

Formal statement

theorem BookProof.ChapterPauliSU2.spinorAction_isHermitian (T : Matrix (Fin 2) (Fin 2) ℂ)
    {X : Matrix (Fin 2) (Fin 2) ℂ} (hX : Xᴴ = X) :
    (spinorAction T X)ᴴ = spinorAction T X := by sorry

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