Characterization for the general solution to a system of matrix equations with quadruple variables

摘要

In this paper, we give some necessary and sufficient conditions for the solvability to the system of matrix equations(0.1)A1X1=C1,X2B1=D1A2X3=C2,X3B2=D2,A3X4=C3,X4B3=D3,A4X1+X2B4+C4X3D4+C5X4D5=E1and provide an expression of the general solution to (0.1). Furthermore, we obtain the maximal and minimal ranks of X3 and X4 in (0.1). The findings of this paper extend the known results in the literatures.