The solvability and the exact solution of a system of real quaternion matrix equations

Abstract

In this paper, we establish necessary and sufficient conditions for the solvability of the system of real quaternion matrix equations $$ \left\{ \begin{array} {l}{A}_{1}X=C_{1},~ \\ YB_{1}=D_{1}, \\ A_{2}Z=C_{2},ZB_{2}=D_{2},A_{3}ZB_{3}=C_{3}, \\ A_{4}X+YB_{4}+C_{4}ZD_{4}=E_{1}. \end{array}\right. $$ We also present an expression of the general solution to the system. The findings of this paper widely extend the known results in the literature.