| Powerful符号矩阵的基指数 |
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| 引用本文： | 邵嘉裕,尤利华,单海英.Powerful符号矩阵的基指数[J].同济大学学报(自然科学版),2003,31(12):1490-1494. |
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| 作者姓名： | 邵嘉裕 尤利华 单海英 |
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| 作者单位： | 同济大学,应用数学系,上海,200092 |
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| 基金项目： | 国家自然科学基金资助项目 ( 1983 10 5 0 )，教育部博士点基金资助项目 ( 2 0 0 0 0 2 470 5 ) |
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| 摘 要： | 研究了n阶 powerful符号矩阵及 powerful带号有向图的基指数 .对一类重要的powerful带号有向图 ,即n阶负Cr cockade有向图 ,证明了其基指数总等于d -r 1 (其中d是该有向图的直径 ) ;并在此基础上进一步确定了该类图 (及相应的矩阵类 )的基指数所构成的集合 .还进一步确定了所有n阶 pwerful符号矩阵的基指数所构成的集合就是n阶非负矩阵的幂敛指数所构成的集合
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| 关 键 词： | 符号矩阵 有向图 基指数 |
| 文章编号： | 0253-374X(2003)12-1490-05 |
| 修稿时间： | 2003年1月7日 |
Basis of Powerful Sign Pattern Matrices |
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| SHAO Jia yu,YOU Li hua,SHAN Hai ying.Basis of Powerful Sign Pattern Matrices[J].Journal of Tongji University(Natural Science),2003,31(12):1490-1494. |
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| Authors: | SHAO Jia yu YOU Li hua SHAN Hai ying |
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| Abstract: | We study the basis of powerful sign pattern matrices and powerful signed digraphs of order n .First we show that the base of each negative C r cockade is always equal to d-r 1 (where d is the diameter of the digraph).Based on this result we further determine the basis set of the class of all the negative C r cockades of order n (and the corresponding class of matrices).We also determine the basis set of the class of all the powerful sign pattern matrices of order n by showing that it is equal to the set of indices of convergence of the class of all the nonnegative matrices of order n . |
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| Keywords: | sign pattern matrices directed graph basis |
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