{"title":"The Vandermonde Matrix in the Commutative Case","authors":"A. I. Perov, I. D. Kostrub","doi":"10.1134/S1064562424702041","DOIUrl":null,"url":null,"abstract":"<p>In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702041","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In a complex Banach algebra, under the assumptions of separateness and spectral separateness, invertibility conditions for the Vandermonde matrix are formulated and proved. Necessary and sufficient conditions for the invertibility of the Vandermonde matrix are given. Analogues of Sylvester’s theorem are formulated.
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