The common solution to system of eight linear real quaternion matrix equations with applications

Abstract

In this paper, we consider a system of eight matrix equations over the real quaternion algebra. We study some necessary and sufficient conditions for the existence of a solution to this
system and give an expression of the general solution to the system when the solvability conditions satisfied, also we express some necessary and sufficient conditions by ranks of coefficients matrices. We present centrosymmetric solution to certain system of quaternion matrix equations. Moreover, we give a numerical example to illustrate our results.