The *congruence class of the solutions of some matrix equations

The *congruence class of a least square solution for the following matrix equations AX=B,A∗XA=D,AXB=Dand(AXXB)=(EF) is presented. Also, we derive necessary and sufficient conditions for the existence of a least square solution and present a general form of such solutions using the Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD).