Inverse problems for symmetric doubly stochastic matrices whose Sule\u{i}manova spectra are bounded below by 1/2
| Autor: | Gnacik, Michal, Kania, Tomasz |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.laa.2020.01.029 |
| Popis: | 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 $\lambda_2, \ldots, \lambda_n$ are non-positive real numbers with $1 + \lambda_2 + \ldots + \lambda_n \geqslant 1/2$, then there exists a symmetric, doubly stochastic matrix whose spectrum is precisely $(1, \lambda_2, \ldots, \lambda_n)$. 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. Comment: Accepted to Linear Algebra and Its Applications, pages 12 |
| Databáze: | arXiv |
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