Generalization of Roth's solvability criteria to systems of matrix equations

Andrii Dmytryshyn, Vyacheslav Futorny, Tetiana Klymchuk +1

W.E. Roth (1952) proved that the matrix equation $AX-XB=C$ has a solution if and only if the matrices $\left[\begin{array}{cc}A& C\\ 0& B\end{array}\right]$ and $\left[\begin{matrix}A&0…