Solution of Certain Matrix Equations
JOHN H. JONES · Proceedings of the American Mathematical Society · 1972
The main purpose of this paper is to obtain solutions of matrix equations of the following types, $AX - XB = C,XDX + AX + XB + C = 0$, in which case $X$ is an unknown $n$ by $n$ matrix and $A,B,C,D$ are $n$ by $n$ matrices having elements belonging to the field $C$ of complex numbers. Results obtained extend those of W. E. Roth, J. E. Potter and others concerning the existence and the representation of solutions $X$ of the above equations.