关于非负矩阵的反特征值问题

华东师范大学学报(自然科学版) ›› 2009, Vol. 2009 ›› Issue (4): 35-38.

关于非负矩阵的反特征值问题

镡松龄

华东师范大学~~数学系，上海\; 200241

收稿日期:2009-01-12 修回日期:2009-03-06 出版日期:2009-07-25 发布日期:2009-07-25
通讯作者: 镡松龄

Inverse eigenvalue problem for nonnegative matrices

SHAN Song-ling

Department of Mathematics, East China Normal University, Shanghai}\, 200241

Received:2009-01-12 Revised:2009-03-06 Online:2009-07-25 Published:2009-07-25
Contact: SHAN Song-ling

摘要/Abstract

摘要： 应用多项式的伙伴矩阵, 对于任意复数~$\lambda, $ 构造出了三阶非负方阵,
使~$\lambda$~为其一特征值, 并证明所给出的是满足条件的含零元素最多的矩阵.

关键词: 非负矩阵, 反特征值, 伙伴矩阵, 非负矩阵, 反特征值, 伙伴矩阵

Abstract: For any given complex number $\lambda$, this paper proved that there exists a
3 by 3 nonnegative matrix
\textbf{\emph{A}} with at least 4 zero entries such that $\lambda$ is an eigenvalue of \textbf{\emph{A}}.
The number 4 of zero entries here is the largest possible.

Key words: inverse eigenvalue, companion matrix , nonnegative matrices, inverse eigenvalue, companion matrix

中图分类号:

O151. 21

镡松龄. 关于非负矩阵的反特征值问题[J]. 华东师范大学学报(自然科学版), 2009, 2009(4): 35-38.

SHAN Song-ling. Inverse eigenvalue problem for nonnegative matrices[J]. Journal of East China Normal University(Natural Sc, 2009, 2009(4): 35-38.