摘要
讨论了矩阵方程（ＡＴＸＡ，ＢＴＸＢ）＝（Ｃ，Ｄ）的对称半正定解．利用广义奇异值分解导出了该矩阵方程有对称半正定解的充分必要条件。
The symmetric positive semidefinite solutions of the matrix equation (ATXA,BTXB)=(C,D) is considered in this paper. Necessary and sufficient conditions for the matrix equation to have symmetric positive semidefinite solutions are derived using the generalized singularvalue decomposition. The expression for the general symmetric positive semidefinite solution is given when certain conditions hold.
出处
《湖南师范大学自然科学学报》
CAS
1997年第4期10-13,29,共5页
Journal of Natural Science of Hunan Normal University
基金
国家自然科学基金
关键词
数值代数
对称半正定解
矩阵方程
奇异值
numerical algebra
matrix
equation
symmetric positive semidefinite solution
