一类非对称矩阵的最大密度指数集  

The Index Set of Maximum Density for a Class of Non-symmetric Matrix

作　　者：李毓祁[1] 

机构地区：[1]中国人民银行海南省五指山市支行,海南五指山572200

出　　处：《海南大学学报（自然科学版）》2003年第3期222-226,共5页Natural Science Journal of Hainan University

摘　　要：证明了至少有一对非零对称元但非对称且周期为2的n阶非本原不可约布尔矩阵所成的类的最大密度指数集是:(ⅰ)若n(>3)是偶数,则Hn={2,3,4,5,…,2n-5,2n-4};(ⅱ)若n(>3)是奇数,则Hn={m∶2≤m≤2n-4且2｜m}.In this paper,the author completely determines the index set of maximum density for the class of n order nonsymmetric imprimitive irreducible Boolean matrix with at least one pair of nonzero symmetry entries and whose given period is two. The main results are the following :(ⅰ)if n(>3) is even, then Hn={2,3,4,5,...,2n-5,2n-4};(ⅱ)if n(>3) is odd, then  Hn={m∶2≤m≤2n-4 and m is even}.

关 键 词：非对称矩阵 最大密度指数集 不可约布尔矩阵 伴随有向图 非零对称元 置换矩阵 

分 类 号：O151.21[理学—数学]