矩阵方程（A^＊XA，B^＊XB）=（C，D）有复半正定解的条件  

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

作　　者：周立仁[1] 

机构地区：[1]湖南理工学院数学学院,湖南岳阳414006

出　　处：《湖南理工学院学报（自然科学版）》2009年第4期13-17,共5页Journal of Hunan Institute of Science and Technology(Natural Sciences)

基　　金：湖南省教育厅一般资助项目(08C395)

摘　　要：研究了复矩阵方程(A*XA,B*XB)=(C,D)有复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)有复半正定解的充分必要条件,同时给出了通解表达式.A study of the complex matrices solutions with complex positive semidefinite solution for the matrix equation（A^＊XA,B^＊XB）=（C,D） is made. 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 obtained.

关 键 词：矩阵方程 复半正定 Hermite半正定 广义奇异值分解 

分 类 号：O151.21[理学—数学]