矩阵方程A^TXA=B的中心对称解及其最佳逼近

The Centro-symmetric Solutions of Matrix Equation A^TXA=B and its Optimal Approximation

利用矩阵的广义奇异值分解 ,得到了线性矩阵方程ATXA =B有中心对称解的充分必要条件及其通解的表达式 .另外 ,导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 centro symmetric solutions of the linear matrix equation A TXA=B are established. In addition, in the solution set of corresponding equation, the expression of the optimal approximation solution to given matrix is derived.