ON CONJUGACY OF DIAGONALIZABLE INTEGRAL MATRICES

Source abstract

It is shown that under some additional assumption two diagonalizable integral matrices X and Y with only rational eigenvalues are conjugate in GLn(ℤ) if and only if they are conjugate over all localizations. This is used to prove that for a prime p≡3 (mod⁡ 4) the adjacency matrices of the Paley graph and the Peisert graph on p2 vertices are conjugate in GLp2(ℤ), answering a question by Peter Sin [9].