矩阵方程AX+X^TB=C的解

Study on the Solvability of Matrix Equation AX+X^TB=C

摘要: 利用矩阵分解，结合矩阵广义逆理论，研究了矩阵方程AX+X^TB=C有解的条件，得到了方程有解时解的一般表达式。

Abstract: The problem of the solvability for the matrix equation AX+X^TB=C is studied by using the ma-trix decomposition and its Moore-Penrose generalized inverse. Some solvability conditions are obtained and the general expression of its solution is given.