I'm having difficulty figuring out how to solve a matrix quadratic of the form, $AXX + BX = -C$ analytically for $X$. Where $A$, $X$, $B$, and $C$ are $N \times N$ matrices.
I tried using
Solve, but got a message saying the system cannot be solved with methods available to
Solvep. Is there any other way?
If no analytical solution exists, it is possible to derive conditions on when the numerical solution exists?