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  • On the sum of two largest eigenvalues of a symmetric matrix [Elektronski vir]
    Ebrahimi, Javad ...
    D. Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple graph is at most the number of vertices of the graph. This can be proved, in particular, for all ... regular graphs. Gernert's conjecture was recently disproved by one of the authors [V. Nikiforov, Linear combinations of graph eigenvalues, Electron. J. Linear Algebra 15 (2006) 329-336], who also provided a nontrivial upper bound for the sum of two largest eigenvalues. In this paper we improve the lower and upper bounds to near-optimal ones, and extend results from graphs to general non-negative matrices.
    Vir: Preprint series. - ISSN 1318-4865 (Vol. 47, št. 1075, 2009, str. 1-8)
    Vrsta gradiva - e-članek
    Leto - 2009
    Jezik - angleški
    COBISS.SI-ID - 15049561

    Povezava(-e):

    http://www.imfm.si/preprinti/PDF/01075.pdf

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