任意体上矩阵广义逆的反序律

Reverse Order Laws for Generalized Inverses of Matrices on An Arbitrary Skew Field

证明了任意体上矩阵乘积的一条分解定理.利用该分解定理作为工具,获得了任意体上矩阵乘积的g一逆和自反g-逆的反序律的充分必要条件.

In this paper, we prove a decomposition theorem of matrix pair over an arbitrary skew field. By applying the decomposition theorem, we obtain some neccessary and sufficient conditions of reverse order laws for g-inverse and reflexive g-inverse of matrix products on an arbitrary skew field.