一类广义非负循环矩阵的逆谱问题  

Inverse spectral problem for a class of generalized nonnegative circulant matrices

作　　者：徐伟孺[1] 雷英杰[1] 顾先明[2] 

机构地区：[1]中北大学理学院,山西太原030051 [2]电子科技大学数学科学学院,四川成都611731

出　　处：《湖北大学学报（自然科学版）》2013年第1期33-37,55,共6页Journal of Hubei University：Natural Science

基　　金：国家自然科学基金(11071227)资助

摘　　要：非负矩阵的逆谱问题是:确定一个n元复数组σ=(λ0;λ1,…,λn-1)是某个n阶非负矩阵的谱的充要条件.结合广义循环矩阵的性质,对一类非负r-循环矩阵的逆谱问题进行讨论,给出它有解的充要条件及其构造性算法,并在此基础上进行推广,继而给出非负中心对称循环矩阵逆谱问题有解的充要条件及其构造性算法.最后结合具体实例证实其算法的有效性和实用性.The nonnegative inverse spectral problem was to determine the necessary and sufficient conditions, where the nonnegative matrix had a given set σ of n complex numbers as its spectra. Based on the properties of generalized circulant matrices, it discussed the inverse spectral problem for a class of nonnegative r-circulant matrices and gave the necessary and sufficient conditions of solvability for this problem and constructive algorithms. Furthermore, the authors gave an extention to nonnegative centrosymmetric circulant matrices on this basis, then the necessary and sufficient conditions of solvability for this problem and constructive algorithms were also given. Finally, some concrete examples confirmed the validity and practicability of these algorithms.

关 键 词：广义循环矩阵 非负r-循环矩阵 非负中心对称循环矩阵 逆谱问题 构造性算法 

分 类 号：O151[理学—数学]