矩阵方程(A~*XA,B~*XB)=(C,D)有Hermite半正定解的条件

Solvability Conditions with Hermite Positive Semidefinite Solution of the Matrix Equation(A~*XA,B~*XB)=(C,D)

研究了复矩阵方程(A~*XA,B^XB)=(C,D)有Hermite半正定解的可解性条件.利用广义奇异值分解,导出了矩阵方程(A~*XA,B~*XB)=(C,D)有Hermite半正定解的充分必要条件,同时给出了通解的表达式.

The complex matrices solutions with Hermite positive semidefinite solution for the matrix equation （A^＊XA,B^＊XB）=（C,D） are investigated. The necessary and sufficient conditions for the existence of such solutions are derived by using the generalized singular value decomposition. The forms of general solution are also presented.