李茜,邵燕灵,高玉斌.一类新的极小谱任意符号模式[J].数学研究及应用,2008,28(2):389~395 |
一类新的极小谱任意符号模式 |
A New Class of Minimally Spectrally Arbitrary Sign Patterns |
投稿时间:2007-05-10 修订日期:2008-01-02 |
DOI:10.3770/j.issn:1000-341X.2008.02.020 |
中文关键词: 符号模式 蕴含幂零 谱任意模式. |
英文关键词:sign pattern potentially nilpotent spectrally arbitrary pattern. |
基金项目:国家自然科学基金(No.10571163); 山西省自然科学基金(No.20041010; 2007011017). |
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中文摘要: |
若给定任意一个$n$次首一实系数多项式$f(\lambda)$,都存在一个实矩阵$B\in Q(A)$, 使得$B$的特征多项式为$f(\lambda)$,则称$A$为谱任意符号模式. 如果一个谱任意符号模式的任意非零元被零取代后所得到的符号模式不是谱任意,那么这个谱任意符号模式称为极小谱任意符号模式.本文证明一类极小谱任意符号模式. |
英文摘要: |
If every monic real polynomial of degree $n$ can be achieved as the characteristic polynomial of some matrix $B\in Q(A)$, then sign pattern $A$ of order $n$ is a spectrally arbitrary pattern. A sign pattern $A$ is minimally spectrally arbitrary if it is spectrally arbitrary but is not spectrally arbitrary if any nonzero entry (or entries) of $A$ is replaced by zero. In this article, we give some new sign patterns which are minimally spectrally arbitrary for order $n\geq 9$. |
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