Abstract
Matrix factorizations brings many conveniences and advantages for solving some real-life problems and for computational processes. The purpose of this paper is to provide a more general perspective on the factorizations and eigenvalues of the matrices whose elements are special number sequences. With the help of some useful techniques, we give factorizations of the (r, k)-bonacci and inverse (r, k)-bonacci matrices. Also, we obtain Cholesky factorization of the symmetric (r, k)-bonacci matrices. Moreover, we obtain upper and lower bounds of the eigenvalues of the symmetric (r, k)-bonacci matrices by using doubly stochastic matrices and the theory of majorization. Finally, we provide some numerical results in order to confirm theoretical results for the special cases of r and k.
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Köme, C. Factorizations and eigenvalues of the (r, k)-bonacci matrices. Comp. Appl. Math. 42, 185 (2023). https://doi.org/10.1007/s40314-023-02331-9
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DOI: https://doi.org/10.1007/s40314-023-02331-9