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In article <1992Sep10.135654.5001@cronkite.ocis.temple.edu> neilfp@astro.ocis.temple.edu (Neil F. Palumbo) writes:
>I am trying to solve the matrix equation XAY+XB+CY+D=0 analytically for the
>unknown matrices {X,Y}. Anyone have any ideas, suggestions, comments ...?

Much depends on the dimensions of the matrices involved.  For example,
if X is a column vector and Y is a row vector, then there is no
solution unless D is of rank one.  Again, if everything is square, any
X and Y satisfying Y = -(XA + C)^{-1}(XB + D) is a solution.  I think
you may have inadvertently left out some important information about
the problem.

Pete Stewart

In the equation:
           
             XAY+XB+CY+D=0,

the dimensions are: A(nxn), B(nxm), C(mxn), D(mxm), X(mxn), Y(nxm), with
 n > m. Furthermore, there is a required structure for the solutions {X,Y}.
X must be of the structure:

		| xx xx .. xx 0  0 ..................................0 |
		| 0  0 ....0 .xx xx .. xx 0 .........................0 |
                | 0  0 ................0  xx xx .. xx 0 .............0 |
                | .................................................... |
                | .................................................... |
                | 0  0 ................................. 0 xx xx .. xx |

and Y must be of the structure X' (note Y not = X'). Any suggestions??