摘要
本文给出了任意体上的矩阵方程ＡＸ—ＹＢ＝Ｃ相容的两个充要条件，并给出了其一般解的表达式，从而推广了域上的Ｗ．Ｅ．Ｒｏｔｈ定理．
In this paper, two necessary and sufficient conditions are established for solvability of the matrix equation Am×s X - YBt×n = Cm×n over an arbitrary skew field.The expression of the gneral solution of the equation is also found.
关键词
Roth定理
矩阵方程
解
体
相容
skew field, matrix equation, generalized inverse of matrix.
