反无效对问题和强无效交错特性

IF 1 3区数学 Q1 MATHEMATICS

Linear Algebra and its Applications Pub Date : 2024-07-18 DOI:10.1016/j.laa.2024.07.014

Aida Abiad , Bryan A. Curtis , Mary Flagg , H. Tracy Hall , Jephian C.-H. Lin , Bryan Shader

{"title":"反无效对问题和强无效交错特性","authors":"Aida Abiad , Bryan A. Curtis , Mary Flagg , H. Tracy Hall , Jephian C.-H. Lin , Bryan Shader","doi":"10.1016/j.laa.2024.07.014","DOIUrl":null,"url":null,"abstract":"<div>The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as <math><mo>(</mo><mi>null</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mi>null</mi><mo>(</mo><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo><mo>)</mo></math>, where <math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math> is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.</div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"699 ","pages":"Pages 539-568"},"PeriodicalIF":1.0000,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The inverse nullity pair problem and the strong nullity interlacing property\",\"authors\":\"Aida Abiad , Bryan A. Curtis , Mary Flagg , H. Tracy Hall , Jephian C.-H. Lin , Bryan Shader\",\"doi\":\"10.1016/j.laa.2024.07.014\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as <math><mo>(</mo><mi>null</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>,</mo><mi>null</mi><mo>(</mo><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo><mo>)</mo></math>, where <math><mi>A</mi><mo>(</mo><mi>i</mi><mo>)</mo></math> is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.</div>\",\"PeriodicalId\":18043,\"journal\":{\"name\":\"Linear Algebra and its Applications\",\"volume\":\"699 \",\"pages\":\"Pages 539-568\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2024-07-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Linear Algebra and its Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0024379524003045\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379524003045","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

逆特征值问题研究的是对角线以外的条目为零-非零模式的矩阵之间可能存在的频谱，这些频谱由图形的邻接性描述。在本文中，我们将矩阵的-空性对称为，其中，是去掉第-行和列后得到的矩阵。逆-空性对问题适用于完整图、循环和树。引入了强无效性交错属性，并开发了相应的超图公设和去交错公设，作为构造具有给定无效性对的矩阵的新工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

The inverse nullity pair problem and the strong nullity interlacing property

The inverse eigenvalue problem studies the possible spectra among matrices whose off-diagonal entries have their zero-nonzero patterns described by the adjacency of a graph G. In this paper, we refer to the i-nullity pair of a matrix A as $(null (A), null (A (i))$ , where $A (i)$ is the matrix obtained from A by removing the i-th row and column. The inverse i-nullity pair problem is considered for complete graphs, cycles, and trees. The strong nullity interlacing property is introduced, and the corresponding supergraph lemma and decontraction lemma are developed as new tools for constructing matrices with a given nullity pair.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Linear Algebra and its Applications 数学-应用数学

CiteScore

2.20

自引率

9.10%

发文量

333

审稿时长

13.8 months

期刊介绍： Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.