A cyclic determinant in two variables

Proved

WorkbookRestored.plus_2271

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

For all complex numbers $x,y$ ,

\det\begin{pmatrix}y&x&x+y\\x+y&y&x\\x&x+y&y\end{pmatrix}=2(x^3+y^3).

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_2271 (Apache-2.0).

Preamble

import Mathlib.Analysis.Complex.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.Trace
open Matrix

Formal statement

theorem WorkbookRestored.plus_2271 (x y : ℂ) : Matrix.det (![![y, x, x+y],![x+y, y, x],![x, x+y, y]]) = 2 * (x^3 + y^3)   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_2271; original Prove2Me node 1cd95833-479e-4707-b429-79b1d0f6409c; Apache-2.0

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