The Minimum Rank of Nonnegative Irreducible Patterns

邵燕灵; 高玉斌

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The Minimum Rank of Nonnegative Irreducible Patterns

更新时间：2026-09-14

- The Minimum Rank of Nonnegative Irreducible Patterns
- 非负不可约模式的最小秩(英文)
- Issue 1, Pages: 6-10(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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邵燕灵, 高玉斌. The Minimum Rank of Nonnegative Irreducible Patterns[J]. 2005, (1): 6-10.
DOI：

邵燕灵, 高玉斌. The Minimum Rank of Nonnegative Irreducible Patterns[J]. 2005, (1): 6-10. DOI：

摘要

设A是n阶非负不可约模式.A的最小秩定义为与A有相同符号模式的全体实矩阵的秩的最小值.考虑矩阵序列A

…

….设Ab是第一个重复的矩阵

且记p0是最小的正整数使得Ab=Ab+p.称b为A的基.p为A的周期.本文研究了非负不可约模式的基与最小秩的关系.

Abstract

Let A be an n×n nonnegative irreducible pattern. The minimum rank of A is the minimum of ranks of all real matrices which have the same sign pattern as A. Consider the sequence A

:. Let A

be the first one that is repeated. Write A

b+p

with p0 minimal. Then b is called the base of A. and p the period of A. We study the relations between the base and the minimum rank of nonnegative irreducible pattern A.

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references

　BrualdiRA,RyserHJ.CombinatorialMatrixTheory[M].CambridgeUniversityPress,1991.

　JohnsonCR.Someoutstandingproblemsinthetheoryofmatrices[J].LinearandMultilinearAlgebra,1982,12:99-108.

　ChenG,HallF,LiZ,WeiB.Onranksofmatricesassociatedwithtree[J].GraphsandCombinatorics,2003,19:323-334.

　LiZ,HallF,EschenbachC.Ontheperiodandbaseofasignpatternmatrix[J].LinearAlgebraAppl.,1994,212/213:101-120.

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