A short note on the order of the Zhang-Liu matrices over arbitrary fields

Abstract

We give necessary and sufficient conditions for the Zhang-Liu matrices to be diagonalizable over arbitrary fields and provide the eigen-decomposition when it is possible. We use this result to calculate the order of these matrices over any arbitrary field. This generalizes a result of the second author.

Keywords: Pascal Matrix, cyclic group orders, eigenvectors, binomial coefficients, finite fields