New solvable conditions and a new expression of the general solution to a system of linear matrix equation over an arbitrary division ring (Q815176)

The authors consider the system of matrix equations \(A_1X=C_1\), \(XB_2=C_2\), \(A_3XB_3=C_3\) over an arbitrary division ring \(F\). They find new necessary and sufficient conditions for its solvability, and they present its general solution. They do the same also for the two particular cases \(A_3=I\) and \(B_3=I\), for the three systems obtained from the above one by skipping off one of the three equations, and for the system \(XB_j=C_j\), \(j=1,2\).