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.