A Quaternion Matrix Equation with Two Different Restrictions

In this paper, we use the equivalence canonical form of four quaternion matrices to consider two systems of quaternion matrix equations. We derive some practical necessary and sufficient conditions for the existence of a solution to these two systems in terms of ranks of the quaternion matrices involved. We also give the general solutions to the systems when the solvability conditions are satisfied. Moreover, we present some numerical examples to illustrate the results of this paper.