Linearlization of Generalized Fibonacci Sequences

Abstract

In this paper, we give linearization of generalized Fibonacci sequences {g n } and {q n }, respectively, defined by Eq.(5) and Eq.(6) below and use this result to give the matrix form of the nth power of a companion matrix of {g n } and {q n }, respectively. Then we reprove the Cassini's identity for {g n } and {q n }, respectively.