体上的矩阵方程sum from i=1 to l A_iXB_i=E

THE MATRIX EQUATION sum from i=1 to 1 A_iXB_i=E OVER A SKEW FIELD

给出了体上的矩阵方程sum from i=l to l A_iXB_i=E有解的充要条件、通解表达式和一种实用解法。

A necessary and sufficient condition for the existence and the expression of gen- eral solution of the matrix equation sum from i=1 to l A_i XB_i=E over a skew field are given. A practical method of solving the equation is also presented.