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

0521939 - MÚ 2021 RIV US eng J - Journal Article
Gnacik, M. - Kania, Tomasz
Inverse problems for symmetric doubly stochastic matrices whose Suleimanova spectra are bounded below by 1/2.
Linear Algebra and Its Applications. Roč. 592, May (2020), s. 175-187. ISSN 0024-3795. E-ISSN 1873-1856
R&D Projects: GA ČR(CZ) GJ19-07129Y
Institutional support: RVO:67985840
Keywords : bistochastic matrix * doubly stochastic matrix * inverse problem * Suleĭmanova spectrum
OECD category: Pure mathematics
Impact factor: 1.401, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.laa.2020.01.029

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.
Permanent Link: http://hdl.handle.net/11104/0306485