关于迹非零对称矩阵本原指数集的另法刻画  

Another method to completely characterize exponent set for class of symmetric matrix with nonzero trace

作　　者：李毓祁 李大超[2] 

机构地区：[1]海南省五指山市人民银行,海南五指山572200 [2]海南师范学院数学系,海南海口571158

出　　处：《海南师范学院学报（自然科学版）》2005年第2期99-103,共5页Journal of Hainan Normal University:Natural Science

摘　　要：运用不同于文[1]的证明方法,对迹非零对称矩阵的本原指数集作出了完全刻画.所得结论是:①把迹非零对称矩阵类SBn按照矩阵的迹划分为互不相交的两大子类:SBn=SBn(Ⅰ)∪SBn(Ⅱ),SBn(Ⅰ)∩SBn(Ⅱ)=Φ;②以无向图G的直径d(G)为参数,确定出子类SBn(Ⅰ)的本原指数集E1={1,2,…,n-1}和子类SBn(Ⅱ)的本原指数集E2={2,3,…,2n-2}\S,其中S是{n,n+1,…,2n-2}中的所有奇数之集;③进而刻画出迹非零对称矩阵类SBn的本原指数集En=E1∪E2={1,2,…,2n-2}\S.We applied the method different from document [ 1 ] to completely characterize the exponent set for the class of symmetric primitive maaix with nonzero trace. Our results were as follows： （ 1 ）We divided the class of symmetric primitive matrix with its nonzero trace into two subclasses by the trace of matrix： SBn=SBn（Ⅰ）∪SBn（Ⅱ）,SBn（Ⅰ）∩SBn（Ⅱ）=Ф（ empty set ） ; （2） We took the diameter d（G） of the graph G as a parameter to determine the exponent set El of the subclass SBn （ Ⅰ ） and the exponent set E2 of the subclass SB. （ Ⅱ ）, that is, E1 = { 1,2,…, n - 1 } and E2 = { 2,3,…,2 n - 2 } ／ S, S is the set of odd, and all the odd of s belongs to the set { n, n ＋ 1, … ,2n - 2} ; （3）And then we determined the exponent set En of the class SBn, that is, En = E1 ∪ E2 = { 1,2,… ,2n - 3} ／ S.

关 键 词：矩阵的迹 本原矩阵 本原指数 局部本原指数 伴随有向图 

分 类 号：O157.5[理学—数学]