Skip to content

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

Research output: Contribution to journalArticlepeer-review

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
Volume592
Early online date23 Jan 2020
DOIs
Publication statusPublished - 1 May 2020

Documents

  • 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

Related information

Activities

Relations Get citation (various referencing formats)

ID: 18258494