5伴随矩阵数值范围边界上的平坦部分

IF 0.7 4区数学 Q2 Mathematics

Electronic Journal of Linear Algebra Pub Date : 2023-02-09 DOI:10.13001/ela.2023.7209

Swastika Saha Mondal, Sarita Ojha, R. Birbonshi

{"title":"5伴随矩阵数值范围边界上的平坦部分","authors":"Swastika Saha Mondal, Sarita Ojha, R. Birbonshi","doi":"10.13001/ela.2023.7209","DOIUrl":null,"url":null,"abstract":"The number of flat portions on the boundary of the numerical range of $5 \\times 5$ companion matrices, both unitarily reducible and unitarily irreducible cases, is examined. The complete characterization on the number of flat portions of a $5 \\times 5$ unitarily reducible companion matrix is given. Also under some suitable conditions, it is shown that a unitarily irreducible $5 \\times 5$ companion matrix cannot have four flat portions on the boundary of its numerical range. This gives a partial affirmative answer to the conjecture given in [3] for $n = 5$. Numerical examples are provided to illustrate the results.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Flat portions on the boundary of the numerical range of a 5 × 5 companion matrix\",\"authors\":\"Swastika Saha Mondal, Sarita Ojha, R. Birbonshi\",\"doi\":\"10.13001/ela.2023.7209\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The number of flat portions on the boundary of the numerical range of $5 \\\\times 5$ companion matrices, both unitarily reducible and unitarily irreducible cases, is examined. The complete characterization on the number of flat portions of a $5 \\\\times 5$ unitarily reducible companion matrix is given. Also under some suitable conditions, it is shown that a unitarily irreducible $5 \\\\times 5$ companion matrix cannot have four flat portions on the boundary of its numerical range. This gives a partial affirmative answer to the conjecture given in [3] for $n = 5$. Numerical examples are provided to illustrate the results.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-02-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2023.7209\",\"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.2023.7209","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: 2

摘要

研究了$5乘5$伴随矩阵的数值范围边界上的平坦部分的数量，这两种情况都是酉可约和酉不可约的。给出了一个$5乘5$酉可约伴随矩阵的平坦部分数的完全刻画。此外，在一些适当的条件下，证明了一个单位不可约的$5乘5$伴随矩阵在其数值范围的边界上不可能有四个平坦部分。这对[3]中给出的$n=5$的猜想给出了部分肯定的答案。数值算例说明了结果。

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

Flat portions on the boundary of the numerical range of a 5 × 5 companion matrix

The number of flat portions on the boundary of the numerical range of $5 \times 5$ companion matrices, both unitarily reducible and unitarily irreducible cases, is examined. The complete characterization on the number of flat portions of a $5 \times 5$ unitarily reducible companion matrix is given. Also under some suitable conditions, it is shown that a unitarily irreducible $5 \times 5$ companion matrix cannot have four flat portions on the boundary of its numerical range. This gives a partial affirmative answer to the conjecture given in [3] for $n = 5$. Numerical examples are provided to illustrate the results.

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

Electronic Journal of Linear Algebra 数学-数学

CiteScore

1.20

自引率

14.30%

发文量

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.