具有负元素矩阵的Perron-Frobenius性质  

Perron-Frobenius Property of Matrices Having Some Negative Entries

作　　者：郑艳萍[1] 宋儒瑛[1] 

机构地区：[1]太原师范学院数学系,太原030012

出　　处：《太原科技大学学报》2010年第3期239-242,共4页Journal of Taiyuan University of Science and Technology

摘　　要：利用算子理论方法结合矩阵分块技巧给出具有负元素矩阵及Perron-Frobenius性质的实矩阵的刻画,同时也讨论了该矩阵的性质。给出以下两个结果新的证明:(1)若A∈Rn×n,则下列性质等价。(ⅰ)A和AT具有强的Perron-Frobenius性质;(ⅱ)A是最终正的;(ⅲ)AT是最终正的。(2)若A是伪-M-矩阵,则A-1∈PFn.In this paper,by using the operator theory and the technique of the operator block,we study the matrix which possesses the Perron-Frobenius property having some negative entries.The following results have been given new proof. （1）For A∈R^n×n,we establish three equivalent properties as follows： （i） Both matrices A and A^T possess the strong Perron-Frobenius property. （ii）A is an eventually positive matrix. （iii）A^T is an eventually positive matrix. （2）IF A∈R^n×n is pseudo-M-matrix,then A^-1∈PFn.

关 键 词：PERRON-FROBENIUS性质 最终正的 伪-M-矩阵 

分 类 号：O177.1[理学—数学]