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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00521939" target="_blank" >RIV/67985840:_____/20:00521939 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.laa.2020.01.029" target="_blank" >https://doi.org/10.1016/j.laa.2020.01.029</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2020.01.029" target="_blank" >10.1016/j.laa.2020.01.029</a>

Result language
angličtina
Original language name
Inverse problems for symmetric doubly stochastic matrices whose Suleimanova spectra are bounded below by 1/2
Original language description
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+λ2+…+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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GJ19-07129Y" target="_blank" >GJ19-07129Y: Linear-analysis techniques in operator algebras and vice versa</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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