A Class of Inertia of Sign Pattern Matrix with Zero Diagonal

雷英杰; 高玉斌

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A Class of Inertia of Sign Pattern Matrix with Zero Diagonal

更新时间：2026-09-14

- A Class of Inertia of Sign Pattern Matrix with Zero Diagonal
- 一类具有零对角的符号模式的惯量
- Issue 3, Pages: 167-170(2005)
- 作者机构：
  
  1. ,山西,太原,030051
  2. 中北大学应用数学系
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2005
- 稿件说明：
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雷英杰, 高玉斌. A Class of Inertia of Sign Pattern Matrix with Zero Diagonal[J]. 2005, (3): 167-170.
DOI：

雷英杰, 高玉斌. A Class of Inertia of Sign Pattern Matrix with Zero Diagonal[J]. 2005, (3): 167-170. DOI：

摘要

　一个n阶符号模式矩阵A称为惯量唯一模式

如果属于符号模式A的所有矩阵都具有相同的惯量.本文基于反对称矩阵的谱集

采用正交相似变换

得到一类具有零对角的符号模式矩阵具有唯一惯量的结论.

Abstract

An n×n sign pattern matrix A is a unique inertia pattern

if all matrices with sign pattern A have the same inertia. Based on the spectral set of skew-symmetric matrix

the result that a class sign pattern matrix with zero diagonal is unique inertia was proved by using orthogonal similarity transformation.

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references

　高玉斌.符号模式矩阵与线性方程组的符号可解性[J].华北工学院学报,2000,21(3):237-242.GaoYubin.Signpatternmatricesandsignsolvabilityoflinearsystems[J].JournalofNorthChinaInstituteofTechnology,2000,21(3):237-242.(inChinese)

　雷英杰,高玉斌.关于次对角模式矩阵惯量的若干性质[J].华北工学院学报,2003,24(5):375-377.LeiYingjie,GaoYubin.Somepropertiesontheinertiaofsubdiagonalsignpatternmatrix[J].JournalofNorthChinaInstituteofTechnology,2003,24(5):375-377.(inChinese)

　周树荃,戴华.代数特征值反问题[M].河南:河南科学技术出版社,1991.202-203.

　EschenbachCA,HallF,LiZ.Signpatternmatricesandgeneralizedinverses[J].LinearAlgebraAppl.,1994,211:53-66.

　YuBinGao,YanlingShao.Inertiallyarbitrarypatterns[J].LinearandMultilinearAlgebra,2001,49:161-168.

　HallFJ,LiZ.Inertiasetsofsymmetricsignpatternmatrices[J].Numer.Math.J.ChineseUniv.,2001,10(2):226-240.

　杨戈峰.实对称三对角矩阵的特征值的估算[J].广东财经职业学院学报,2002(2):71-74.YangGefeng.Estimateofeigenvalueontherealsymmetricthiplediagonalmatrix[J].JournalofGuangdongVocationalCollegeofFinanceandEconomics,2002(2):71-74.(inChinese)

　李庆杨.数值分析[M].武汉:华中科技大学出版社,2003.236-242.

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