A New Aspect of Dual Fibonacci Quaternions

Abstract

Dual Fibonacci quaternions are first defined by [5]. In fact, these quaternions must be called as dual coefficient Fibonacci quaternions. In this paper, dual Fibonacci quaternions are redefined by using the dual quaternions given in [16]. Since the generalization of the complex numbers is the real quaternions, the generalization of the dual numbers is the dual quaternions. Also, we investigate the relations between the dual Fibonacci and the Lucas quaternion which connected the Fibonacci and Lucas numbers. Furthermore, we give the Binet's formulas and Cassini identities for these quaternions.