The common solution to six quaternion matrix equations with applications

摘要

We in this paper establish necessary and sufficient conditions for the existence of and an explicit expression for a common solution to six classical linear quaternion matrix equations A1X = C1, XB1 = C2, A2X = C3, XB2 = C4, A3XB3 = C5, and A4XB4 = C6. As applications, symmetric, persymmetric and centrosymmetric solutions to certain systems of quaternion matrix equations are presented. Furthermore, we give an example to illustrate the result of this paper. Some known results can be regarded as the special cases of this paper.