一个矩阵方程反问题的研究

On a inverse problem for matrix equation

设A、B、C都是m×n阶矩阵,当A和B满足同时奇异值分解时,文中解决了一个关于X,Y的矩阵方程的反问题,对称解,而且给出了有解的充分必要条件,也给出了它的极小Frobe-nius范数对称解.

In this paper, the problem for matrix equation of X, Y was solued, when A and B satisfy the same singular value decomposition （SSVD）. The symetric solution and the sufficient and necessary conditions were obtained and the minimum - Frobenius - norm symmetric solution was given.