Applied Sciences

Permanent URI for this communityhttps://hdl.handle.net/11693/115470

Browse

Browsing Applied Sciences by Subject "(0, 1)-matrix"

Filter results by typing the first few letters
Now showing 1 - 1 of 1
  • Thumbnail Image
    ItemOpen Access
    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.