{"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}
引用次数: 0
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 $\gamma$.
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