半环上矩阵的广义逆与T-序

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.