On Fibonacci quaternion matrix

Abstract

In this study, we have defined Fibonacci quaternion matrix and investigated its powers. We have also derived some important and useful identities such as Cassini’s identity using this new matrix.

The Complex-type Narayana-Fibonacci Numbers

“…Algebraically reducing sequences, many of its features such as the generating matrix, generating function, Binet formula, exponential, permanental, and combinatorial representations have been studied and continue to be studied by many scientists. We can give (Shannon and Bernstein, 1973;Shannon and Horadam, 1994;Lee, 2000;Stakhov and Rozin, 2006;Gogin and Myllari, 2007;Ozkan, 2007;Yılmaz and Bozkurt, 2009;Tasci and Firengiz, 2010;Tuglu et al, 2011;Akuzum and Deveci, 2021;Halici and Deveci, 2021;Erdag et al, 2022) studies as an example of the current ones among these studies. In many of these studies, matrices corresponding to reduced sequences have been used to obtain various results.…”

A novel public key cryptography based on generalized Lucas matrices

“…Halici, et.al. [6], discussed the Fibonacci quaternion matrix by considering entries as n-th Fibonacci quaternion number and derived some identities like Cassini's identity, Binet formula, ...etc. In [19] Stanimirovic, et.al defined a generalization of Fibonacci and Lucas matrices whose elements are defined by the general second-order non-degenerated sequence and in some cases, they also obtained inverse for those matrices.…”