除环上矩阵的Γ逆

Γ-inverse of Matrix over Skew Field

该文研究除环Ｄ上矩阵的Γ逆，主要结果是：（１）对于Ｄ上自共轭对合矩阵Ｐ，Ａ∈Ｈｎ×ｍ关于Ｐ的Γ｛１，２，３，４｝逆Ａｐ＋г存在的充要条件是秩ＡＡ＝秩ＡＡ＝秩Ａ，推广了相应结论；（２）将域上矩阵｛１｝逆、｛２｝逆及｛１，２｝逆的集合刻划推广到Ｄ上矩阵相应的Γ逆．

n this paper we study the Γ-inverse of matrix over a skew field D,and get the following results: (1) Matrix A has a Γ{ 1,2,3,4 }inverse for a self-conjugate involution matrix P,over D if and only if rank(AA)=rank(A A)=rankA. It extend previous result;(2) The characterizations of A (1},A {2} and A {1, 2}over an arbitrary field are extend to a skew field D respectively.