迹为零的对称本原矩阵的scrambling指数  

The Scrambling Index of Zero-Trace Symmetric Primitive Matrices

作　　者：张月梅[1] 陈佘喜[1] 

机构地区：[1]湖南科技大学数学与计算科学学院,湖南湘潭411201

出　　处：《河南科学》2011年第2期136-138,共3页Henan Science

基　　金：湖南省科学技术厅科技计划(2010FJ3166);湖南科技大学2010年研究生创新基金资助项目(S100125)

摘　　要：设A为n阶本原矩阵,若存在正整数k,使得对于Ak的任意两行,都在某一列上的元素为正,这样的最小正整数称为本原矩阵A的scrambling指数.采用图理论来研究对称本原A的scrambling指数.解决了迹为零的对称本原矩阵的scrambling指数的上确界问题,进而得到了其指数集,并完全刻划了这类矩阵的极矩阵.The scrambing index of a primitive matrix A is the smallest positive integer k such that any two rows of Ak have at least one positive element in a coincident position.In this paper,the scrambing index of symmetric primitive matrices by using graph theory were investigated.The upper bound for the scrambing index of zero-trace symmetric primitive matrices was obtained.Moreover,the scrambing index set for this class of matrices was determined,and characterize completely the extremal matrices.

关 键 词：本原矩阵 SCRAMBLING指数 本原指数 有向图 

分 类 号：O157[理学—数学]