体上二次矩阵方程的解

Solution to a Second Order Matrix Equation Over a Skew Field

本文得到了体上二次矩阵方程XAY= B有解的充要条件.并给出了当r(A)= r(B)时矩阵方程XAY= B的通解.

In this paper, necessary and sufficientconditions are given for a m atrix equation ofXAY= B type to have solutions, and gives the generalrepresentation form ula ofthe solutions.