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Inverse problems for symmetric doubly stochastic matrices whose Suleĭmanova spectra are bounded below by 1/2

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A new sufficient condition for a list of real numbers to be the spectrum of a symmetric doubly stochastic matrix is presented; this is a contribution to the classical spectral inverse problem for symmetric doubly stochastic matrices that is still open in its full generality. It is proved that whenever λ2,…,λn are non-positive real numbers with 1 + λ+…+ λn ⩾ 1/2, then there exists a symmetric, doubly stochastic matrix whose spectrum is precisely (1, λ2,…,λn). We point out that this criterion is incomparable to the classical sufficient conditions due to Perfect-Mirsky, Soules, and their modern refinements due to Nader et al. We also provide some examples and applications of our results.
Original languageEnglish
Pages (from-to)175-187
JournalLinear Algebra and its Applications
Early online date23 Jan 2020
Publication statusPublished - 1 May 2020


  • SDIEP_revised_gnacik_kania

    Accepted author manuscript (Post-print), 490 KB, PDF document

    Due to publisher’s copyright restrictions, this document is not freely available to download from this website until: 23/01/21

    Licence: CC BY-NC-ND

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