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Abstract
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 λ_{2},…,λ_{n} are nonpositive real numbers with 1 + λ_{2 }+…+ λ_{n} ⩾ 1/2, then there exists a symmetric, doubly stochastic matrix whose spectrum is precisely (1, λ_{2},…,λ_{n}). We point out that this criterion is incomparable to the classical sufficient conditions due to PerfectMirsky, Soules, and their modern refinements due to Nader et al. We also provide some examples and applications of our results.
Original language  English 

Pages (fromto)  175187 
Journal  Linear Algebra and its Applications 
Volume  592 
Early online date  23 Jan 2020 
DOIs  
Publication status  Published  1 May 2020 
Keywords
 doubly stochastic matrix
 bistochastic matrix
 inverse problem
 SDIEP
 Suleĭmanova spectrum
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Dive into the research topics of 'Inverse problems for symmetric doubly stochastic matrices whose Suleĭmanova spectra are bounded below by 1/2'. Together they form a unique fingerprint.Activities
 1 Invited talk

Talk at Networks Seminar in the Mathematical Institute of University of Oxford
Michal Gnacik (Speaker)
10 Nov 2020Activity: Talk or presentation types › Invited talk