矩阵方程(XA,XB)=(C,D)的对称解、半正定解和亚半正定解

SYMMETRIC,SEMI-DEFINITE AND SEMIPOSITIVE SUBDEFINITE SOLUTIONS OF MATRIX EQUATION(XA,XB)=(C,D)

给出了矩阵方程(XA,XB)=(C,D)有对称解、半正定解和亚半正定解的充分必要条件;在有解的情况下,给出了通解的表达方式.

The necessary and sufficient conditions for thd matrix equation (XA,XB)=(C,D) having symmetric, semi-definite and semipositive subdefinite solutions are studied. The explicit expression for general solutions are also given when the conditions hold.