几乎可约矩阵关于幂敛指数的极阵的特征表述

Characterization of the Extremal Matrices About Indices of Convergence in Nearly Reducible Matrices

本文证明了:(1)当n≠2p时,M(n,p)中幂敛指数值为M(n,p)的几乎可约矩阵在置换相似下是唯一的。(2)当n=2p时,M(n,p)中幂敛指数值为M(n,p)的几乎可约矩阵在置换相似下是[p/2]个,并给出相应的图的构造。

In this paper, we prove that the matrice in M(n,p), whose indice is the upper bound M(n,p), is unique in a sense, where n≠2P, and give a graphic characterization of the matrices in M(n,p), whose indices are the upper bound M(n,p), where n=2P.