关于环上长方矩阵的加权群可逆性  

On weighted group invertibility for rectangular matrices over an arbitrary ring

作　　者：章劲鸥[1] 

机构地区：[1]宁波大学数学系,浙江宁波315211

出　　处：《纯粹数学与应用数学》2013年第2期146-154,共9页Pure and Applied Mathematics

基　　金：宁波市自然科学基金(2012A610034)

摘　　要：研究任意环上长方矩阵的加权群逆和加权{1,5}-逆。利用矩阵分解,得到了长方矩阵积的加权群逆存在的一些等价条件和计算方法及任意环上长方矩阵的加权{1,5}-逆的刻画表达式。得到的定理推广了有关方阵群逆和{1,5}-逆的相关结果。结果还可适合应用于加法范畴中的态射。The weighted group inverses of rectangular matrices and the weighted （1, 5^-inverse of a rectangular matrix over an arbitrary ring are studied. Using Matrix decomposition method,First, the weighted group inverse of a rectangular matrix product PAQ for which there exist pi and QI such that PPA = A = AQQ＇ can be characterized and computed. Moreover, the expressions are given for the weighted （1, 5）-inverse of a rectangular matrix over an arbitrary ring. This generalizes recent results obtained for the group inverse of square matricesand the weighted （1, 5）-inverse of a rectangular matrix over an arbitrary ring. The results also apply to morphisms in （additive） categories.

关 键 词：环 长方矩阵 von Neumann正则 加权群逆 

分 类 号：O153.3[理学—数学]