Half Off Diagonal det

Proved

D1Bound5.halfOffDiagonal_det

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Exact reference determinant, obtained from the rank-one determinant lemma rather than a computer expansion of twenty-four permutation terms.

Preamble

import Mathlib.Analysis.CStarAlgebra.Matrix
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.Permutation
import Mathlib.LinearAlgebra.Matrix.SchurComplement
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_RootMatrixOperatorBound_Definitions

Formal statement

section
open scoped Matrix.Norms.L2Operator
open Matrix

namespace D1Bound5













theorem _root_.D1Bound5.halfOffDiagonal_det : halfOffDiagonal.det = (-3/16 : ℂ) := by sorry





end D1Bound5
end

Source

D1Bound5/ReferenceMatrixSpectral.lean, lines 41-60, SHA-256 a9d2534dbab31dc06c160d4476f3546ac57b74623f0a03cba8eaeb8e7e822001. Project: https://github.com/tomislav-math/d1-bound5-lean

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