`BookProof.ShiftedQuadraticMatrix.rotConj_det` {O : Matrix (Fin d) (Fin d) ℝ} (hO : Oᵀ * O = 1) (c : Fin d → ℝ) : (rotConj O c).det = ∏ i, c i

Proved

BookProof.ShiftedQuadraticMatrix.rotConj_det

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterShiftedQuadraticMatrixEsa.

BookProof.ShiftedQuadraticMatrix.rotConj_det {O : Matrix (Fin d) (Fin d) ℝ} (hO : Oᵀ * O = 1) (c : Fin d → ℝ) : (rotConj O c).det = ∏ i, c i

Formalization note: Lean 4 identifier BookProof.ShiftedQuadraticMatrix.rotConj_det.

Preamble

-- Generated from ChapterShiftedQuadraticMatrixEsa.lean — theorem BookProof.ShiftedQuadraticMatrix.rotConj_det
import Definitions.Def_ChapterHermiteProductCore
import Definitions.Def_ChapterHermiteProductBasis
import Definitions.Def_ChapterNavierStokesDifferentialL2
import Definitions.Def_ChapterHyperbolicQuadraticEsa
import Definitions.Def_ChapterQuadraticRotationEsa
import Definitions.Def_ChapterShiftedHermiteCore
import Definitions.Def_ChapterShiftedQuadraticEsa
import Definitions.Def_ChapterFarisLavine
import Definitions.Def_ChapterStoneBridge
import Definitions.Def_ChapterEsaClosureCore
import Definitions.Def_ChapterSirkTrotterKato
import Mathlib
import Definitions.Def_ChapterShiftedQuadraticMatrixEsa
open BookProof.ShiftedQuadraticMatrix



open MeasureTheory MvPolynomial Matrix
open BookProof.HermiteProductCore BookProof.HermiteProductBasis
open BookProof.NavierStokesFlow.DifferentialL2
open BookProof.HyperbolicQuadratic
open BookProof.QuadraticRotation
open BookProof.ShiftedHermiteCore
open BookProof.ShiftedQuadratic
open BookProof.FarisLavine
open BookProof.StoneBridge BookProof.EsaClosure BookProof.ChapterStoneResolvent

noncomputable section

variable {d : ℕ}

Formal statement

theorem BookProof.ShiftedQuadraticMatrix.rotConj_det {O : Matrix (Fin d) (Fin d) ℝ} (hO : Oᵀ * O = 1) (c : Fin d → ℝ) :
    (rotConj O c).det = ∏ i, c i := by sorry

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