{"title":"Norm behavior of Jordan and bidiagonal matrices","authors":"G. Krishna Kumar, P. V. Vivek","doi":"10.1007/s43036-024-00378-x","DOIUrl":null,"url":null,"abstract":"<div><p>Determining the norm behavior of non-normal matrices from the sets related to the spectrum is one of the fundamental problems of matrix theory. This article proves that the pseudospectra and condition spectra determine the norm behavior of Jordan matrices for any matrix <i>p</i>-norm. Further, sufficient conditions for determining the 1-norm and infinity norm behavior of bidiagonal matrices from the pseudospectra and condition spectra are also provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00378-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Determining the norm behavior of non-normal matrices from the sets related to the spectrum is one of the fundamental problems of matrix theory. This article proves that the pseudospectra and condition spectra determine the norm behavior of Jordan matrices for any matrix p-norm. Further, sufficient conditions for determining the 1-norm and infinity norm behavior of bidiagonal matrices from the pseudospectra and condition spectra are also provided.
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