More Identities for Fibonacci and Lucas quaternions

Abstract

In this paper, we de…ne the associate matrix asBy the means of the matrix F; we give several identities about Fibonacci and Lucas quaternions by matrix methods. Since there are two di¤erent determinant de…nitions of a quaternion square matrix (whose entries are quaternions), we obtain di¤erent Cassini identities for Fibonacci and Lucas quaternions apart from Cassini identities that given in the papers [5] and [7].

On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions

“…. More studies about the quaternions can be found in [3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”

Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients

“…For instance, in [5], Cerda-Morales studied generalized hybrid Fibonacci numbers and their properties. In [6], using an associate matrix, Irmak gave various identities about Fibonacci and Lucas quaternions by matrix methods. In [7], Kızılates ¸investigated the q-Fibonacci and the q-Lucas hybrid numbers and gave some algebraic properties of these numbers.…”

Dual-complex generalized k-Horadam numbers

“…respectively. Recently, many researchers have studied several applications and generalizations of the number sequences(see [6,7,[11][12][13][14][15]21,22,24]). Yazl¬k and Taşkara introduced the generalized k Horadam sequence, which is generalization of many number sequences in the literature [24].…”