半环上矩阵的广义逆与T-序  

Generalized inverse and T-Ordering of matrices over semirings

作　　者：郭倩茹[1] 李培[1] 

机构地区：[1]西北大学数学系,陕西西安710127

出　　处：《纺织高校基础科学学报》2011年第1期109-113,共5页Basic Sciences Journal of Textile Universities

基　　金：陕西省教育厅专项基金资助项目(2007JK413);西北大学科学研究基金资助项目(09NW25)

摘　　要：引入了半环上矩阵Moore-Penrose逆的概念.通过矩阵的T-序关系探讨半环上矩阵的Moore-Penrose逆,得到了矩阵满足T-序条件的若干性质,并且得到Moore-Penrose逆是其他广义逆的最大元或最小元.研究了幂等的非负偏序半环上的矩阵,得到了一个很有用的结论.Firstly the concept of the Moore-Penrose inverse was introduced.Moore-Penrose inverse of the matrices over semirings was researched by T-orderings relationship of the matrix.Several properties of satisfied T-orderings condition of the matrix was gotten.Moreover,Moore-Penrose inverse was the large element of other generalized inverse or minimum element.Finally,the matrix of non-negative idempotent partial-orders semiring was studied.A useful conclusion was obtained.

关 键 词：半环 偏序半环 矩阵 MOORE-PENROSE逆 T-序关系 

分 类 号：O152.7[理学—数学]