Max-代数上线性方程组的解集[EB/OL]
北京：中国科技论文在线
） 摘要： 本文讨论max-代数上线性方程A×x=b的求解问题, 与传统线性系统一样, max-代数上的线性方程系统的解分为无解, 有唯一解及有无穷多解三种情况
当方程有唯一解时, 本文给出了max-代数上线性方程系统的类似于经典线性代数中的Cramer法则, 当方程有无穷多个解时, 本文证明了max-代数上线性方程系统的极小解的存在性, 并给出了极小解的构造公式
最后, 当方程有无穷多个解时给出了求max-代数上线性方程所有解的算法
线性方程系统
Wang Huili （ College of Mathematics and Software Science, SiChuan Normal University, ChenDu 610066
解集
） Abstract： This paper deals with the max-algebraic linear equation system A×x=b
As in the conventional linearalgebra such a linear system may have none, exactly one orinfinitely many solutions
When the number of solutions is exactlyone, Cramer's rule is given as an analogue of the classical linearalgebra
When the number of solutions is infinite, the existence ofa minimal solution is shown and the formula of minimal solution isgiven
Furthermore, it is proved that every solution can beexpressed as a linear combination of a respective minimal solutionand somespecial vectors
Finally, an algorithm to describe all the solutions of a given max-algebraic linear equation system is obtained when its number of solutions is infinite
Keywords： Max-algebra; Linear equation system; Solution set; Minimal solution; Cramer's rule 下载PDF阅读器 PDF全文下载： 初稿 （ 165 ） 原始数据 作者简介： Wang Xueping, (1965-), male, professor, major research direction: Fuzzy relational equation, Theory of lattices, Linear algebra in semirings
通信联系人： 【收录情况】 中国科技论文在线： 王学平
极小解
Cramer法则 Wang Xueping *
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