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    Öğe
    Eigenvalues and eigenvectors of a certain complex tridiagonal matrix family
    (Hacettepe Univ, Fac Sci, 2014) Oteles, Ahmet; Akbulak, Mehmet
    In this paper, we obtain the eigenvalues and eigenvectors of a certain complex tridiagonal matrix family in terms of the Chebyshev polynomials of the first kind.
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    Jacobsthal Numbers and Associated Hessenberg Matrices
    (Univ Waterloo, 2018) Oteles, Ahmet; Karatas, Zekeriya Y.; Zangana, Diyar O. Mustafa
    In this paper, we define two n x n Hessenberg matrices, one of which corresponds to the adjacency matrix of a bipartite graph. We then investigate the relationships between the Hessenberg matrices and the Jacobsthal numbers. Moreover, we give Maple algorithms to verify our results.
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    On the connectivity properties and energy of Fibonomial graphs
    (Elsevier, 2014) Akbulak, Mehmet; Kale, Akin; Oteles, Ahmet
    We introduce a new type of graph called a Fibonomial graph, denoted G(n). Entries of the adjacency matrix of G depend on the well-known Fibonomial coefficients modulo 2. We investigate the connectivity properties, eigenvalues, and energy of G(n). We lastly obtain the sum of the Laplacian eigenvalues of G(n). (C) 2013 Elsevier B.V. All rights reserved.
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    Positive integer powers of certain complex tridiagonal matrices
    (Elsevier Science Inc, 2013) Oteles, Ahmet; Akbulak, Mehmet
    In this paper, we firstly present a general expression for the entries of the rth (r is an element of N) power of a certain n-square complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain a complex factorization formula for generalized Fibonacci-Pell numbers obeying also classical Fibonacci and Pell numbers. (C) 2013 Elsevier Inc. All rights reserved.
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    Öğe
    Positive Integer Powers of One Type of Complex Tridiagonal Matrix
    (Malaysian Mathematical Sciences Soc, 2014) Oteles, Ahmet; Akbulak, Mehmet
    In this paper, we firstly present a general expression for the entries of the rth (r is an element of N) power of a certain n-square complex tridiagonal matrix, in terms of the Chebyshev polynomials of the first kind. Secondly, we obtain two complex factorizations for Fibonacci and Pell numbers. We also give some Maple 13 procedures in order to verify our calculations.