{"title":"霍恩逆问题","authors":"J. Queiró, A. P. Santana","doi":"10.13001/ela.2023.7539","DOIUrl":null,"url":null,"abstract":"Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\\gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $\\gamma$.","PeriodicalId":50540,"journal":{"name":"Electronic Journal of Linear Algebra","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The inverse Horn problem\",\"authors\":\"J. Queiró, A. P. Santana\",\"doi\":\"10.13001/ela.2023.7539\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\\\\gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $\\\\gamma$.\",\"PeriodicalId\":50540,\"journal\":{\"name\":\"Electronic Journal of Linear Algebra\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Linear Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.13001/ela.2023.7539\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Linear Algebra","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.13001/ela.2023.7539","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
Alfred Horn关于Hermitian矩阵和的特征值猜想是在20多年前证明的。在本文中，给出了求解多面体中的$n$-元组$\gamma$，构造具有所需谱的Hermitian矩阵，使得它们的和具有特征值$\gamma$的问题。
Alfred Horn's conjecture on eigenvalues of sums of Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\gamma$ in the solution polytope, constructing Hermitian matrices with the required spectra such that their sum has eigenvalues $\gamma$.
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