域上矩阵积的广义逆及自反广义逆的逆反律  

REVERSE ORDER LAW FOR GENERALIZED INVERSES AND REFLEXIVE GENERALIZED INVERSES OF PRODUCTS OF MATRICES OVER ARBITRARY FIELDS

作　　者：刘淑丹[1] 游宏[1] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001

出　　处：《数学年刊（A辑）》2004年第4期523-530,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金;黑龙江省自然科学基金

摘　　要：令A,B是任意域上的矩阵且使得AB有意义。本文研究了AB的广义逆、自反广义逆与A,B的广义逆、自反广义逆的积之间的关系,得到了B{1}A{1}(AB){1},B{1}A{1}=(AB){1},B{1,2}A{1,2}(AB){1,2}和B{1,2}A{1,2}=(AB){1,2}成立的一些充要条件。Let A and B be matrices over an arbitrary field such that AB exists. The relationship between generalized inverses, reflexive generalized inverses of AB and the products of generalized inverses, reflexive generalized inverses of A, B have been studied in this paper. The authors derive some necessary and sufficient conditions for B{1}A{1} (AB){1},B{1}A{1}=(AB){1}, B{1, 2}A{1, 2} (AB){1, 2} and B{1, 2}A{1, 2}=(AB){1, 2}.

关 键 词：G-逆 自反g-逆 二个矩阵的积 域 

分 类 号：O151.21[理学—数学]