Department of Information Systems and Technologies

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Browsing Department of Information Systems and Technologies by Subject "(0, 1)-matrix"

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    On a conjecture of Ilmonen, Haukkanen and Merikoski concerning the smallest eigenvalues of certain GCD related matrices
    (Elsevier Inc., 2016) Altinişik, E.; Keskin, A.; Yildiz, M.; Demirbüken, M.
    Let Kn be the set of all n×n lower triangular (0,1)-matrices with each diagonal element equal to 1, Ln={YYT:Y ∈ Kn} and let cn be the minimum of the smallest eigenvalue of YYT as Y goes through Kn. The Ilmonen-Haukkanen-Merikoski conjecture (the IHM conjecture) states that cn is equal to the smallest eigenvalue of Y0Y0 T, where Y0 ∈ Kn with (Y0)ij = (Formula presented.) for i > j. In this paper, we present a proof of this conjecture. In our proof we use an inequality for spectral radii of nonnegative matrices. © 2015 Elsevier Inc.