`BookProof.ChapterWignerLittleGroup.sq_two` (M : Matrix (Fin 2) (Fin 2) ℂ) : M * M = M.trace • M - M.det • (1 : Matrix (Fin 2) (Fin 2) ℂ)

Proved

BookProof.ChapterWignerLittleGroup.sq_two

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterWignerLittleGroup.

BookProof.ChapterWignerLittleGroup.sq_two (M : Matrix (Fin 2) (Fin 2) ℂ) : M * M = M.trace • M - M.det • (1 : Matrix (Fin 2) (Fin 2) ℂ)

Formalization note: Lean 4 identifier BookProof.ChapterWignerLittleGroup.sq_two.

Preamble

-- Generated from ChapterWignerLittleGroup.lean — theorem BookProof.ChapterWignerLittleGroup.sq_two
import Mathlib
import Definitions.Def_ChapterWignerLittleGroup
open BookProof.ChapterWignerLittleGroup


open Matrix Complex

Formal statement

theorem BookProof.ChapterWignerLittleGroup.sq_two (M : Matrix (Fin 2) (Fin 2) ℂ) :
    M * M = M.trace • M - M.det • (1 : Matrix (Fin 2) (Fin 2) ℂ) := by sorry

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