一对特殊矩阵的联合谱半径的有限步实现

The Finite-step Realization of the Joint Spectral Radius of a Pair of n × n Special Matrices

一个矩阵集具有有穷性是说这个矩阵集中的矩阵内积的最大增长率在一定周期内可以得到.主要研究了一对方阵集的联合/广义谱半径的有限步可实现性,即任意的两个n×n实方阵S1,S2所组成的矩阵集S={S1,S2},矩阵S1中的元素都大于0,而矩阵S2相似于一个对角矩阵,且S2中的所有非零元素都具有相同的符号,证明了矩阵集S={S1,S2}具有有穷性.

A set of matrices is said to have the finiteness property if the maximal rate of growth of long products of matrices taken from the set can be obtained by a periodic product .It studies the finite-step realization of the joint/generalized spectral radius of a pair of real square matrices .If S={S1 ,S2} where S1,S2 are n×n matrices and S1 =（aij） with aij≥0 and S2 is similar to a diagonal matrix whose nonzero elements have the same sign , S has the finiteness property .