Positive Integer Powers of One Type of Complex Tridiagonal Matrix

Abstract

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.