The reducible solution to a system of matrix equations over the Hamilton quaternion algebra

Abstract

Reducible matrices are closely associated with the connection of directed graph and can be used in stochastic processes, biology and others. In this paper, we investigate the reducible solution to a system of matrix equations over the Hamilton quaternion algebra. We establish the necessary and sufficient conditions for the system to have a reducible solution and derive a formula of the general reducible solution of the system when it is solvable. Finally, we present a numerical example to illustrate the main results of this paper.