关于矩阵方程AX+X^TC=B的解的存在性的探讨

A study of solution existence for matrix equation AX+X^TC=B

以矩阵广义逆为工具 ,给出了矩阵方程AX +XTC =B解的存在的充要条件。将该方程的求解问题转化为对其等价方程的求解 ,得出一些相应的很有价值的结论。并在理论上进行了较为严密的证明 ,同时 ,对该方程的常见的某些特殊情形做了进一步的推导。

This article gives the full and essential condition of the solution existence of the matrix equation AX+X TC=B by the generalized inverse of matrixes.We gain some valuable conclusion by changing this equation into its equal equation, and we strictly prove it in theory.At the same time, we deduce same special situations which often met in the equation further.