Integer Powers of Certain Complex Tridiagonal Matrices and Some Complex Factorizations

Durmus Bozkurt, S Burcu Bozkurt Altındag

In this paper, we obtain a general expression for the entries of the rth power of a certain n × n complex tridiagonal matrix where if n is even, r ∈ Z or if n is odd, r ∈ N. In addition, we get the complex factorizations of Fibonacci polynomials, Fibonacci and Pell numbers.