矩阵方程AXA^T=D的对称与反对称解及其应用

Symmetric, Antri-Symmetric Solutions of Matrix Equation AXAT =D and Application

考虑了矩阵方程AXA^T=D有对称与反对称解的充分必要条件,并给出了通解的表达式。作为应用考虑了矩阵方程AXB^T±BX^TA^T=C有解的充分必要条件,给出了通解的表达式。

The necessary and sufficient conditions for the matrix equation AXAT = D having symmetric and anti-symmetric solutions are studied. The explicit expressions for general solutions are given when the conditions hold. As applications, the necessary and sufficient condition for matrix equation AXBT± BXTAT =C having solution is obtained and the explicit representation of general solution is also given.