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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (1): 116-126    
    
极大加代数的对称代数$\mathbb{S}$上互补基本矩阵
袁跃爽1, 张子龙1,2
1.河北师范大学 数学与信息科学学院, 河北石家庄 050024
2.河北省计算数学与应用重点实验室, 河北石家庄 050024
Complementary basic matrices of the symmetrized algebra of max algebra
YUAN Yue-shuang1, ZHANG Zi-long1,2
1. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
2. Key Lab of Computational Mathematics and Applications of Hebei Province, Shijiazhuang 050024, China
 全文: PDF 
摘要： 主要研究了极大加代数的对称代数$\mathbb{S}$上互补基本矩阵, 给出本征积的概念, 证明了$\mathbb{S}$上的Laplace定理, 由此推出所有互补基本矩阵的行列式相等, 且任意两个互补基本矩阵的行列式中的非零项均一一对应相等. 在一个互补基本矩阵的行列式中, 对于确定非零项的任一置换, 给出了在另一个互补基本矩阵的行列式中找到置换使其确定相同非零项的方法.
关键词： 极大加代数;  对称代数;  互补基本矩阵;  Laplace定理;  行列式    
Abstract: The paper mainly studies the complementary basic matrices in $\mathbb{S}$. It first introduces the concepts of the intrinsic products and proves the Laplace's Theorem in $\mathbb{S}$. Accordingly, the determinants of CB-matrices are the same and for any nonzero term in the determinant of one CB-matrix, there exists an equal term in the determinant of the other CB-matrix and vice versa. By the same time, for a given permutation which determines the nonzero term of the determinant of one CB-matrix, a method is given to find a permutation who determines the same nonzero term in the determinant of the other CB-matrix.
Key words: max algebra    symmetrized algebra    complementary basic matrices    Laplace’s Theorem    determinant
收稿日期: 2015-04-29 出版日期: 2018-05-17
CLC:  O151.21  
基金资助: 国家自然科学基金(11271109)
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袁跃爽
张子龙

引用本文:

袁跃爽, 张子龙. 极大加代数的对称代数$\mathbb{S}$上互补基本矩阵[J]. 高校应用数学学报, 2016, 31(1): 116-126.

YUAN Yue-shuang, ZHANG Zi-long. Complementary basic matrices of the symmetrized algebra of max algebra. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 116-126.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I1/116

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