A Class of Minimally Spectrally Arbitrary Patterns

任国花; 高玉斌

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A Class of Minimally Spectrally Arbitrary Patterns

更新时间：2026-09-14

- A Class of Minimally Spectrally Arbitrary Patterns
- 一类极小谱任意符号模式
- Vol. 32, Issue 4, Pages: 387-391(2011)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2011
- 稿件说明：
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任国花, 高玉斌. A Class of Minimally Spectrally Arbitrary Patterns[J]. 2011, 32(4): 387-391.
DOI：

任国花, 高玉斌. A Class of Minimally Spectrally Arbitrary Patterns[J]. 2011, 32(4): 387-391. DOI：

摘要

对一类恰含2n个非零元的n(n≥5)阶符号模式矩阵A进行了研究

通过分析A的定性矩阵类中任意实矩阵的特征多项式

证明了符号模式矩阵A是蕴含幂零的

并运用N ilpoten t-Jacob ian方法

证明了A及其所有母模式矩阵都是谱任意的

最后证明了A是极小谱任意符号模式矩阵.

Abstract

A class of n×n(n≥5) sign pattern matrices A with exactly 2n nonzero entries is mainly discussed.By analyzing the characteristic polynomial of any real matrix in the qualitative matrix class of A

it is proved that A is potential nilpotent.By using the Nilpotent-Jacobian method

it is proved that sign pattern A and each superpattern of A is spectrally arbitrary.At last it is proved that A is a minimal spectrally arbitrary sign pattern matrix.

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references

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