一类矩阵方程的对称次反对称解及其最佳逼近

The Symmetric and Sub-anti-symmetric Sulutions of Matrix Equation A^TXB=B and ITS Optimal

利用矩阵的广义奇异值分解 ,得到了矩阵方程 ATXA =B有对称次反对称解的充分必要条件及其通解的表达式 ,并且给出了在矩阵方程的解集合中与给定矩阵的最佳逼近解的表达式 .

Using the general singular value decomposition of matrices, the necessary and sufficient conditions for the existence and the expressions for the symmetric and sub-anti-symmetric solutions of the linear matrix equation $ATXA=B$ are established. Furthermore, in the solution set of corresponding equation, the expression of the optimal approximation solution togiven matrix is derived.