{"title":"矩阵的椭圆数值范围","authors":"Wlat Hamad Jalal, Ahmed Muhammad","doi":"10.12988/imf.2020.91282","DOIUrl":null,"url":null,"abstract":"The numerical range W ( T ) of a complex n × n matrix T is the subset W ( T ) = {(cid:104) T x, x (cid:105) : x ∈ C n , and (cid:107) x (cid:107) = 1 } in the complex plane C , where (cid:104) ., . (cid:105) denotes the usual inner product in C . In this paper a series of tests given, allowing one to determine when the numerical range of a 6 × 6 matrix T is an elliptic disc.","PeriodicalId":107214,"journal":{"name":"International Mathematical Forum","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Elliptic numerical range of matrices\",\"authors\":\"Wlat Hamad Jalal, Ahmed Muhammad\",\"doi\":\"10.12988/imf.2020.91282\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The numerical range W ( T ) of a complex n × n matrix T is the subset W ( T ) = {(cid:104) T x, x (cid:105) : x ∈ C n , and (cid:107) x (cid:107) = 1 } in the complex plane C , where (cid:104) ., . (cid:105) denotes the usual inner product in C . In this paper a series of tests given, allowing one to determine when the numerical range of a 6 × 6 matrix T is an elliptic disc.\",\"PeriodicalId\":107214,\"journal\":{\"name\":\"International Mathematical Forum\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematical Forum\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12988/imf.2020.91282\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematical Forum","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12988/imf.2020.91282","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
复n × n矩阵T的数值范围W (T)是复平面C中W (T) = {(cid:104) T x, x (cid:105): x∈C n， (cid:107) x (cid:107) = 1}的子集，其中(cid:104) .，。(cid:105)表示C中的通常内积。本文给出了一系列的检验，使人们能够确定6 × 6矩阵T的数值范围何时为椭圆盘。
The numerical range W ( T ) of a complex n × n matrix T is the subset W ( T ) = {(cid:104) T x, x (cid:105) : x ∈ C n , and (cid:107) x (cid:107) = 1 } in the complex plane C , where (cid:104) ., . (cid:105) denotes the usual inner product in C . In this paper a series of tests given, allowing one to determine when the numerical range of a 6 × 6 matrix T is an elliptic disc.
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