New Properties and Identities for Fibonacci Finite Operator Quaternions

Abstract

In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions. Moreover, we derive many identities related to Fibonacci finite operator quaternions by using the matrix representations.

Keywords

• Fibonacci number
• Fibonacci quaternion
• finite operator
• matrix representation