与某些允许或要求对角化的图相关联的符号模式

IF 0.7 4区 数学 Q2 Mathematics
Sunil Das
{"title":"与某些允许或要求对角化的图相关联的符号模式","authors":"Sunil Das","doi":"10.13001/ela.2022.5557","DOIUrl":null,"url":null,"abstract":"The problems of characterizing sign pattern matrices that allow or require diagonalizability are mostly open. In this paper, we introduce the concept of essential index for a tree sign pattern matrix and use it to investigate the allow problem on diagonalizability for sign pattern matrices having their graphs as trees. We characterize sign pattern matrices allowing diagonalizability, whose graphs are star or path. We also give a sufficient condition for sign pattern matrices whose graphs are trees to allow diagonalizability. Further, we give a necessary condition for a sign pattern matrix to require diagonalizability and characterize all star sign pattern matrices that require diagonalizability.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sign patterns associated with some graphs that allow or require diagonalizability\",\"authors\":\"Sunil Das\",\"doi\":\"10.13001/ela.2022.5557\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The problems of characterizing sign pattern matrices that allow or require diagonalizability are mostly open. In this paper, we introduce the concept of essential index for a tree sign pattern matrix and use it to investigate the allow problem on diagonalizability for sign pattern matrices having their graphs as trees. We characterize sign pattern matrices allowing diagonalizability, whose graphs are star or path. We also give a sufficient condition for sign pattern matrices whose graphs are trees to allow diagonalizability. Further, we give a necessary condition for a sign pattern matrix to require diagonalizability and characterize all star sign pattern matrices that require diagonalizability.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-03-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2022.5557\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2022.5557","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0

摘要

表征允许或要求对角化的符号模式矩阵的问题大多是开放的。在本文中,我们引入了树符号模式矩阵的本质索引的概念,并用它来研究图为树的符号模式矩阵对角化的允许问题。我们刻画了允许对角化的符号模式矩阵,其图是星形或路径。我们还给出了图为树的符号模式矩阵允许对角化的一个充分条件。此外,我们给出了符号模式矩阵需要对角化的一个必要条件,并刻画了所有需要对角化性的星形符号模式矩阵。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sign patterns associated with some graphs that allow or require diagonalizability
The problems of characterizing sign pattern matrices that allow or require diagonalizability are mostly open. In this paper, we introduce the concept of essential index for a tree sign pattern matrix and use it to investigate the allow problem on diagonalizability for sign pattern matrices having their graphs as trees. We characterize sign pattern matrices allowing diagonalizability, whose graphs are star or path. We also give a sufficient condition for sign pattern matrices whose graphs are trees to allow diagonalizability. Further, we give a necessary condition for a sign pattern matrix to require diagonalizability and characterize all star sign pattern matrices that require diagonalizability.
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
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信