- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 69 Issue: 1
- More identities for Fibonacci and Lucas quaternions
More identities for Fibonacci and Lucas quaternions
Authors : Nurettin Irmak
Pages : 369-375
View : 6 | Download : 5
Publication Date : 2020-06-30
Article Type : Research
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