IJPAM: Volume 84, No. 2 (2013)
MATRIX AND THE FIBONACCI POLYNOMIALS
Institute of Mathematics and Quantitative Methods
Faculty of Economics and Administration
University of Pardubice
Studentska 84, Pardubice 532 10, CZECH REPUBLIC
Abstract. Many mathematicians investigated in papers various types of integer matrices the entries of which satisfy a second order recurrence. Some of the authors used methods leading to obtain real or complex factorizations of the Fibonacci or the Lucas numbers. Civciv (2008) computed the determinant of a five-diagonal matrix with the Fibonacci numbers as its entries. His result is given more generally and completely in this paper. It is showed that the determinant of a matrix, the entries of which are the Gibonacci numbers, is related to the values of the Fibonacci polynomial. Calculations are done by using the eigenvalues of the given matrix.
Received: February 20, 2013
AMS Subject Classification: 11B39, 11C20, 15B36
Key Words and Phrases: generalized Fibonacci number, determinant, five-diagonal matrix, eigenvalue, Fibonacci polynomial
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DOI: 10.12732/ijpam.v84i2.10 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395