矩阵方程AX=B,XD=E解的研究

Research to the solution of matrix equation AX = B, XD = E

详细讨论了矩阵方程AX=B,XD=E的各种解,即在相容时的极小范数解;在不相容时分两种情况讨论了最小二乘解,并分别给出了它们解的表达式;最后给出了该矩阵方程在不相容时的极小范数最小二乘解．

In this paper all kinds of solutions for the matrix equation AX = B, XD = E are studied in detail. If the matrix equation AX = B, XD = E is consistent, we give the expression of its minimum-normal solution. If the matrix equation AX = B, XD = E is not consistent, we study its least-squares solution and express its least-squares solution in two cases. Finally we give the minimum-normal and least-squares solution to the matrix equation AX = B, XD = E in inconsistency.