The General Solution to a System of Eight Quaternion Matrix Equations with Applications

摘要

This paper studies some necessary and sufficient conditions for the existence of a solution and gives an expression of the general solution to the system of eight linear quaternion matrix equations. As an application, necessary and sufficient conditions are given for the system of certain matrix equations to have a symmetric solution. Note that in some of the mentioned conditions we use rank equalities. In addition, some numerical examples are given.