Powerful符号矩阵的基指数  

Basis of Powerful Sign Pattern Matrices

作　　者：邵嘉裕[1] 尤利华[1] 单海英[1] 

机构地区：[1]同济大学应用数学系,上海200092

出　　处：《同济大学学报（自然科学版）》2003年第12期1490-1494,共5页Journal of Tongji University:Natural Science

基　　金：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 )

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 .

关 键 词：符号矩阵 有向图 基指数 

分 类 号：O151.21[理学—数学]