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

Abstract

References

  • Koshy, T. Fibonacci and Lucas numbers with applications, Wiley, Newyork, 2001.
  • Horadam, A. F. Complex Fibonacci numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • Iyer, M. R. A note on Fibonacci Quaternions, The Fib. Quarterly, 3 (1969), 225-229.
  • Swamy, M. N. S. On generalized Fibonacci quaternions, The Fib. Quarterly, 5 (1973), 547-550.
  • Halıcı, S. On Fibonacci Quaterions, Adv. Appl. Clifford Algebras, 12 (2012), 321-327.
  • Akyiğit, M., Kösal, H. H., Tosun, M. Split Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 535-545.
  • Akyiğit, M., Kösal, H. H., Tosun, M. Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24 (2014), 631-641.
  • Tan, E., Yılmaz, S., Şahin, M. A new generalization of Fibonacci quaternions, Chaos Solitions Fractals, 82 2016, 1-4.
  • Tan, E., Yılmaz, S., Şahin, M. A Note on bi-periodic Fibonacci and Lucas quaternions, Chaos Solitions Fractals, 85 2016, 138-142.
  • Tan, E., Sahin, M., Yilmaz, S. The generalized bi-periodic Fibonacci quaternions and octonions. Novi Sad J. Math. doi.org/10.30755/NSJOM.07284.
  • Morais, J. P., Georgiev, S., Spröbig, W. Real Quaternionic Calculus Handbook, Birkhauser, London, 2014.

More identities for Fibonacci and Lucas quaternions

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

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}.

References

  • Koshy, T. Fibonacci and Lucas numbers with applications, Wiley, Newyork, 2001.
  • Horadam, A. F. Complex Fibonacci numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70 (1963), 289-291.
  • Iyer, M. R. A note on Fibonacci Quaternions, The Fib. Quarterly, 3 (1969), 225-229.
  • Swamy, M. N. S. On generalized Fibonacci quaternions, The Fib. Quarterly, 5 (1973), 547-550.
  • Halıcı, S. On Fibonacci Quaterions, Adv. Appl. Clifford Algebras, 12 (2012), 321-327.
  • Akyiğit, M., Kösal, H. H., Tosun, M. Split Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 23 (2013), 535-545.
  • Akyiğit, M., Kösal, H. H., Tosun, M. Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24 (2014), 631-641.
  • Tan, E., Yılmaz, S., Şahin, M. A new generalization of Fibonacci quaternions, Chaos Solitions Fractals, 82 2016, 1-4.
  • Tan, E., Yılmaz, S., Şahin, M. A Note on bi-periodic Fibonacci and Lucas quaternions, Chaos Solitions Fractals, 85 2016, 138-142.
  • Tan, E., Sahin, M., Yilmaz, S. The generalized bi-periodic Fibonacci quaternions and octonions. Novi Sad J. Math. doi.org/10.30755/NSJOM.07284.
  • Morais, J. P., Georgiev, S., Spröbig, W. Real Quaternionic Calculus Handbook, Birkhauser, London, 2014.
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Nurettin Irmak 0000-0003-0409-4342

Publication Date June 30, 2020
Submission Date July 4, 2018
Acceptance Date October 31, 2019
Published in Issue Year 2020 Volume: 69 Issue: 1

Cite

APA Irmak, N. (2020). More identities for Fibonacci and Lucas quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69(1), 369-375.
AMA Irmak N. More identities for Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2020;69(1):369-375.
Chicago Irmak, Nurettin. “More Identities for Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69, no. 1 (June 2020): 369-75.
EndNote Irmak N (June 1, 2020) More identities for Fibonacci and Lucas quaternions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69 1 369–375.
IEEE N. Irmak, “More identities for Fibonacci and Lucas quaternions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 69, no. 1, pp. 369–375, 2020.
ISNAD Irmak, Nurettin. “More Identities for Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 69/1 (June 2020), 369-375.
JAMA Irmak N. More identities for Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69:369–375.
MLA Irmak, Nurettin. “More Identities for Fibonacci and Lucas Quaternions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 69, no. 1, 2020, pp. 369-75.
Vancouver Irmak N. More identities for Fibonacci and Lucas quaternions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2020;69(1):369-75.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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