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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (1): 116-126    DOI:
    
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
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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     
Received: 29 April 2015      Published: 17 May 2018
CLC:  O151.21  
  O151.22  
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YUAN Yue-shuang
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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.

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


极大加代数的对称代数$\mathbb{S}$上互补基本矩阵

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 
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