| 坡上矩阵可逆的条件 |
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| 引用本文： | 段俊生.坡上矩阵可逆的条件[J].数学进展,2006,35(3):285-288. |
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| 作者姓名： | 段俊生 |
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| 作者单位： | 天津商学院应用数学科学系,天津,300134 |
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| 基金项目： | The work is supported by the National Natural Science Foundation of China(No.10461005)
the Scientific Research Foundation of Tianjin Education Committee(No. 20050404) |
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| 摘 要： | 坡S是一个元素满足条件s 1=1的交换半环．证明了坡S上n×n矩阵A可逆当且仅当∑k=1 n aik=1(i=1,2,…,n)且aikajk=0(i≠j,k=1,2,…,n)．在坡S中可定义补元,得到S上每一个可逆矩阵是一个置换矩阵当且仅当S不包含不同于0和1的有补元．
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| 关 键 词： | 半环 坡 可逆矩阵 不变式 |
| 文章编号： | 1000-0917（2006）03-0285-04 |
| 收稿时间： | 2004-02-16 |
| 修稿时间： | 2004-09-01 |
Invertible Conditions for Matrices Over an Incline |
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| DUAN Jun-sheng.Invertible Conditions for Matrices Over an Incline[J].Advances in Mathematics,2006,35(3):285-288. |
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| Authors: | DUAN Jun-sheng |
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| Abstract: | An incline S is a commutative semiring satisfying the condition s + 1 = 1 for all s ∈ S. It is proved that an n × n matrix A over an incline S is invertible if and only if ∑nk=1 aik = 1(i = 1, 2,…, n) and aikajk = 0(i ≠ j, k = 1, 2,…, n).Complements can be defined in an incline S and it is obtained that every invertible matrix over S is a permutation matrix if and only if S does not contain elements, distinct from 0 and 1, having a complement. |
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| Keywords: | semiring incline invertible matrix permanent |
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