Generating New Commuting Coprime Matrix Pairs From Known Pairs

Commuting coprime integer matrices arise in signal processing in a number of contexts. This paper develops two ways, one nonlinear and the other linear, to generate new commuting coprime pairs from known pairs. The first method is based on computing powers of the initial pair of matrices, and the second method is based on appropriate types of linear combinations of the initial pair of matrices. This enriches the already known families of coprime matrices reported in recent literature. Several properties of the newly generated coprime pairs are also addressed.