环上长方形矩阵的加权群-Moore-Penrose可逆性  

Weighted group-Moore-Penrose invertibility of rectangular matrices over a ring

作　　者：陈申宝[1] Chen Shenbao(Zhejiang Business Technology Institute,Ningbo 315012,China)

机构地区：[1]浙江工商职业技术学院,浙江宁波315012

出　　处：《纯粹数学与应用数学》2020年第2期239-252,共14页Pure and Applied Mathematics

基　　金：浙江省自然科学基金(L Y15F020010);浙江省教育厅科研项目(Y201636499).

摘　　要：研究了具有对合的环上长方形矩阵的W加权群-Moore-Penrose可逆性。给出了环上长方形矩阵的W加权Moore-Penrose逆和W加权群逆的存在性的特性。环上长方形矩阵的W加权群-Moore-Penrose逆可以被刻画和计算出来。这推广了具有对合的环上平方矩阵的群-Moore-Penrose逆的结果。结果也适用于(加法)范畴中的态射.The W-weighted group-Moore-Penrose invertibility of rectangular matrices over a ring with an involution * are studied. Characterizations are given for existence of the W-weighted Moore-Penrose inverse and the W-weighted group inverse of a rectangular matrix over a ring. The W-weighted group-Moore-Penrose inverse of a rectangular matrix over a ring can be characterized and computed. This generalizes results obtained for the group-Moore-Penrose inverse of a square matrix over a ring with an involution *. The results also apply to morphisms in(additive) categories.

关 键 词：环 von Neumann正则 W加权Moore-Penrose逆 W加权群逆 W加权群-Moore-Penrose逆 

分 类 号：O151.21[理学—数学]