迹非零几乎可约分块布尔矩阵的幂敛指数

The Index of Convergence of Nearly Reducible Block Matrices

设H_n(d)是恰含d个正对角元的n阶几乎可约分块布尔矩阵的集合,1≤d≤n,对任何矩阵A∈H_n(d),本文证明了■其中s_n=|(2n-5-(4n-3)^(1/2))/2|,同时刻画了H_n(d)中幂敛指数达到最大值的极矩阵．

Let Hn（d）, 1 ≤ d≤n, be the set of nearly reducible Boolean block matrices of order n with exact d non-zero diagnols. The index of convergence of a matrix A is denoted by k（A）. This paper solves the problem for the exact upper bound of k（A） completely. The following result is proved： k（vi,vj）≤max{（n-d-2）^2＋2,2n-d-1}≤{（n-d-2）^2 2n-d-1, 1≤d≤sn sn≤dn≤n Sn=[2n-5-√4n-3/2] And we give complete characterization for the extreme matrices with the largest convergent index in Hn（d）.