{"title":"交换情况下的凡德蒙德矩阵","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":531,"journal":{"name":"Doklady Mathematics","volume":"109 3","pages":"216 - 220"},"PeriodicalIF":0.5000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":531,\"journal\":{\"name\":\"Doklady Mathematics\",\"volume\":\"109 3\",\"pages\":\"216 - 220\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1064562424702041\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424702041","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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