Volume 37 • Number 4 • 2014   • Positive Integer Powers of One Type of Complex Tridiagonal Matrix Ahmet Öteleş and Mehmet Akbulak Abstract. In this paper, we firstly present a general expression for the entries of the $r${th }($r\in\mathbb{N}$) 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. 2010 Mathematics Subject Classification: 47B36, 15A18, 65F15, 11B39 Full text: PDF