矩阵方程AXA^T+BYB^T=C的亚正定解

The Subpositive Definite Solutions of Matrix Equation AXA^T+BYB^T=C

利用矩阵对的广义奇异值分解(GSVD),讨论了矩阵方程AXAT+BYBT=C关于亚正定矩阵X、Y有解的充要条件,其中A,B,C是给定的矩阵,在有解时给出了解的通式.

Applying the generalized singular value decompositions（GSVD） of matrices, a necessary and sufficient condition for matrix equation AXA^T＋BYB^T=C having subpositive definite solution is discussed, where A, B, C is given, and the explicit representation of generalized solution is given.