More identities for Fibonacci and Lucas quaternions

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Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
Volume:69 Issue:1
More identities for Fibonacci and Lucas quaternions

More identities for Fibonacci and Lucas quaternions

Authors : Nurettin IRMAK

Pages : 369-375

View : 41 | Download : 8

Publication Date : 2020-06-30

Article Type : Research Paper

Abstract :In this paper, we define the associate matrix as% \begin{equation*} F=\leftinsert ignore into journalissuearticles values( \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 insert ignore into journalissuearticles values(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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