矩阵方程 AXA^T+BYB^T=C的对称正定解  

THE SYMMETRIC POSITIVE DEFINITE SOLUTION OF THE MATRIX EQUATION AXA^T +BYB^T =C

作　　者：刘向华 

机构地区：[1]株洲师专数学系,412007

出　　处：《数学理论与应用》2002年第1期79-82,共4页Mathematical Theory and Applications

摘　　要：本文研究矩阵方程 AXAT+BYBT=C的对称正定解 .利用广义奇异值分解 (GSVD)We study symmetric positive definite solution of the matrix equation AXA T +BYB T =C ,where A is a given real m×n matrix, B is given real m×p matrix,and C is a given real m×m matrix ,whth m,n,p positive integers.By making use of the generalized singular value decomposition,we derive general analytic formulas,and present necessary and sufficient conditions for guaranteeing the existence of the solution.

关 键 词：矩阵方程 对称正定矩阵 广义奇异值分解 解 充分条件 

分 类 号：O151.21[理学—数学] O241.6[理学—基础数学]