Rational Realizations of Inertially Arbitrary Sign Patterns

高玉斌; 邵燕灵

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Rational Realizations of Inertially Arbitrary Sign Patterns

更新时间：2026-09-14

- Rational Realizations of Inertially Arbitrary Sign Patterns
- 惯量任意符号模式的有理数实现
- Issue 3, Pages: 189-192(2007)
- 作者机构：
  
  中北大学理学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2007
- 稿件说明：
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高玉斌, 邵燕灵. Rational Realizations of Inertially Arbitrary Sign Patterns[J]. 2007, (3): 189-192.
DOI：

高玉斌, 邵燕灵. Rational Realizations of Inertially Arbitrary Sign Patterns[J]. 2007, (3): 189-192. DOI：

摘要

设A是一个n阶符号模式

称三元数组的集合i(A)={i(B)|B∈Q(A)}为符号模式A的惯量.若对任意满足r+s+t=n的非负三元数组(r

都有(r

t)∈i(A)

则称A是惯量任意符号模式.本文研究n(n≥2)阶惯量任意符号模式Sn

证明了Sn对任意惯量都存在有理数实现.

Abstract

An n×n sign pattern matrix A is an inertially arbitrary pattern if for each nonnegative triple(r

t) with r+s+t=n

t)∈i(A).This paper considers the n×n(n≥2) inertially arbitrary pattern S

with each upper off-diagonal entry positive

the(1

1) entry negative

the(n

n) entry positive

and every other diagonal entry zero.We prove that there exist rational realizations for the inertia of S

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references

Arav M,Hall F J,Koyuncu S.Rational realizations of the minimum rank of a sign pattern matrix[J].Linear AlgebraAppl.,2005,409:111-125.

Gao Yubin,Shao Yanling.Inertially arbitrary patterns[J].Linear and Multilinear Algebra,2001,49:161-168.

Drew J H,Johnson C R,Olesky D D.Spectrally arbitrary patterns[J].Linear Algebra Appl.,2000,308:121-137.

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