A system of matrix equations with five variables

摘要

In this paper, we give some necessary and sufficient conditions for the consistence of the system of quaternion matrix equations A1X=C1,YB1=D1,A2W=C2,ZB2=D2,A3V=C3,VB3=C4,A4VB4=C5,A5X+YB5+C6W+ZD6+E6VF6=G6,and constitute an expression of the general solution to the system when it is solvable. The outcomes of this paper encompass some recognized results in the collected works. In addition, we establish an algorithm and a numerical example to illustrate the theory constructed in the paper.