Some Results on Homogeneous Matrix Equations
Dietrich von Rosen · SIAM Journal on Matrix Analysis and Applications · 1993
New representations of general solutions to the matrix equations $AXB = 0$ and $A_1 XB_1 = 0$, $A_2 XB_2 = 0$, based on vector space decompositions, are given. In a certain sense the solutions are natural and show an easily interpretable structure. Furthermore, the solutions enable the finding of solutions to $A_1 X_1 B_1 + A_2 X_2 B_2 = 0$ and $A_1 XB_1 = 0$, $A_2 XB_2 = 0$, $A_3 XB_3 = 0$ where for the latter equations no solutions have hitherto been derived. Some other extensions are also considered.