矩阵方程AX-XB=C,AA^-A=A解的讨论

Solution of Matrix Equation AX-XB= C,AA^-A=A

通过线性方程组解的情况,推广到矩阵方程AX-XB=C有解的充要条件以及广义逆矩阵在矩阵方程中的应用.在矩阵方程里引入了广义逆矩阵,通过广义逆矩阵给出了某类矩阵方程的性质和结论.

The paper gives the solution necessary and sufficient condition of the matrix equation AX-XB=C,as well as the generalized inverse matrix in the matrix equation application.The matrix equation introduces the generalized inverse matrix,it gives some kind of matrix equation nature and conclusion through the generalized inverse matrix.