More identities for Fibonacci and Lucas quaternions

Year 2020, Volume: 69 Issue: 1, 369 - 375, 30.06.2020

Nurettin Irmak

Abstract

In this paper, we define the associate matrix as%

\begin{equation*}

F=\left( 

\begin{array}{cc}

1+i+2j+3k & i+j+2k \\ 

i+j+2k & 1+j+k%

\end{array}%

\right) .

\end{equation*}%

By the means of the matrix $F,$ we give several identities about Fibonacci

and Lucas quaternions by matrix methods. Since there are two different

determinant definitions of a quaternion square matrix (whose entries are

quaternions), we obtain different Cassini identities for Fibonacci and Lucas

quaternions apart from Cassini identities that given in the papers \cite%

{halici} and \cite{akyigit2}.

Keywords

Fibonacci Quaternions, Lucas Quaternions, recurrence relations

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