Alma van der Merwe, Madelein Thiersen, Hugo J. Woerdeman
{"title":"The c-numerical range of a quaternion skew-Hermitian matrix is convex","authors":"Alma van der Merwe, Madelein Thiersen, Hugo J. Woerdeman","doi":"10.1007/s43036-024-00391-0","DOIUrl":null,"url":null,"abstract":"<div><p>We show that the <i>c</i>-numerical range of a non-scalar skew-Hermitian quaternion matrix is convex. In fact, included in our result is that the <i>c</i>-numerical range of a skew-Hermitian matrix is a rotation invariant subset of the quaternions with zero real parts.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 4","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00391-0.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Operator Theory","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s43036-024-00391-0","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
We show that the c-numerical range of a non-scalar skew-Hermitian quaternion matrix is convex. In fact, included in our result is that the c-numerical range of a skew-Hermitian matrix is a rotation invariant subset of the quaternions with zero real parts.