由谱确定的双随机矩阵  

Two new kinds of doubly stochastic matrices determined by its spectrum

作　　者：雷英杰[1] 徐玉霞[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《安徽大学学报（自然科学版）》2017年第2期41-46,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金青年基金资助项目(11501528)

摘　　要：求由谱确定的双随机矩阵A:对任意可逆矩阵X和某个置换矩阵P,确定与A相似的所有双随机矩阵X^(-1)AX是否都是P^TAP形式;证明了n阶对称双随机情形下关于由谱确定的矩阵的猜想其逆命题不成立;刻画了n=3时,由谱确定的双随机矩阵的特征;通过分析置换矩阵的特点及其与两种双随机矩阵之间的关系,证明了这两种双随机矩阵都是由谱确定的.The formulation of seeking a doubly stochastic matrixA determined by its spectrum （DS） is. for arbitrary reversible matrixX , if the doubly stochastic matrices X-lAX that are similar to A are of the form pTAp for some permutation matrix P. In this paper, we proved that the inverse proposition of the conjecture about DS symmetric doubly stochastic matrices was false and characterized 3 order doubly stochastic matrices that were DS. Finally, by analyzing the characteristics of permutation matrices and the relationship between two kinds of doubly stochastic matrices , we proved that the prescribed two kinds of doubly stochastic matrices were determined by the spectrum.

关 键 词：双随机矩阵 置换矩阵 由谱确定的 

分 类 号：O151.2[理学—数学]