ELA, Volume 13, pp. 153-156, June 2005, abstract.

Solution of Linear Matrix Equations in a 
*Congruence Class

Roger A. Horn, Vladimir V. Sergeichuk, 
and Naomi Shaked-Monderer

The possible *congruence classes of a square solution 
to the real or complex linear matrix equation AX=B are 
determined. The solution is elementary and self contained, 
and includes several known results as special cases, 
e.g., X is Hermitian or positive semidefinite, and X 
is real with positive definite symmetric part.