SavedAdd your journal

Journals / Düzce Üniversitesi Bilim ve Teknoloji Dergisi / 2019 / Cilt: 7 - Sayı: 1

Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices

Kuaterniyon Matrisleri ile Bazı Fibonacci ve Lucas Kuaterniyon Özdeşlikleri

Bahar DEMİRTÜRK BİTİM
Pages
606–615
Publication Date
2022-10-12
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Our object is to derive some identities concerning Fibonacci and Lucas quaternions by using some new quaternion matrices with terms Fibonacci and Lucas numbers.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we consider one of the most known Fibonacci matrix Q and the Fibonacci quaternion matrix MQFn, where Qn is the n-th Fibonacci quaternion.
📊
Key Findings & Data:In particular we define some new quaternion matrices.
💡
Conclusion & Impact:Our object is to derive some identities concerning Fibonacci and Lucas quaternions by using some new quaternion matrices with terms Fibonacci and Lucas numbers.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fibonacci sayıları · Lucas sayıları · Fibonacci kuaterniyonları

Abstract

In this paper, we consider one of the most known Fibonacci matrix Q and the Fibonacci quaternion matrix MQFn, where Qn is the n-th Fibonacci quaternion. In particular we define some new quaternion matrices. Our object is to derive some identities concerning Fibonacci and Lucas quaternions by using some new quaternion matrices with terms Fibonacci and Lucas numbers.

Özet

Bu makalede en çok bilinen Fibonacci matrislerinden biri olan Q matrisi ve Qn n. Fibonacci kuaterniyonu olmak üzere MnQF Fibonacci kuaterniyon matrisi ele alınmıştır. Ayrıca bazı yeni kuaterniyon matrisleri tanımlanmıştır. Bu çalışmada terimleri Fibonacci ve Lucas kuaterniyonları olan yeni kuaterniyon matrislerini kullanarak, Fibonacci ve Lucas kuaterniyonları ile ilgili bazı özdeşlikler elde edilecektir.

🔖

Cite This Article

BİTİM, B. D. (2022). Some Identities of Fibonacci and Lucas Quaternions by Quaternion Matrices. Düzce Üniversitesi Bilim ve Teknoloji Dergisi, Cilt: 7 - Sayı: 1, 606–615. https://ajindex.com/articles/494411

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (12)

  1. B. Demirtürk Bitim and N. Topal, “Quaternions via generalized Fibonacci and Lucas number components,” Mat. Rep., accepted 24.04.2017
  2. S. Halıcı, “On Fibonacci quaternions”, Adv. Appl. Clifford Algebr., vol. 22, no. 2, pp. 321-327, 2012
  3. S. Halıcı, “On complex Fibonacci quaternions,” Adv. Appl. Clifford Algebr., vol. 23, no. 1, pp.105-112, 2013
  4. W. R. Hamilton, Elements of Quaternions, London, Longmans and Green, 1866
  5. A. F. Horadam, “Complex Fibonacci numbers and Fibonacci quaternions,” Amer. Math. Monthly, vol. 70, pp. 289-291, 1963
  6. A. F. Horadam, “Quaternion recurrence relations,” Ulam Quarterly, vol. 2, no. 2, pp. 23-33, 1993
  7. M. R. Iyer, “Some results on Fibonacci quaternions”, Fibonacci Quart., vol. 7, pp. 201-210, 1969
  8. R. Keskin, B. Demirtürk, “Some new Fibonacci and Lucas identities by matrix methods”, Internat. J. Math. Ed. Sci. Tech., vol. 41, no. 3, pp. 379-387, 2009
  9. T. Koshy, Fibonacci and Lucas Numbers with Applications, New York, John Wiley & Sons, 2001
  10. B. K. Patel and P. K. Ray, “On the properties of (p,q) -Fibonacci and (p,q) -Lucas quaternions,” Mat. Rep., vol. 21, no. 1, pp. 1-10, 2019
  11. P. Ribenboim, My Numbers, My Friends, New York, Springer Verlag, 2000
  12. S. Vajda, Fibonacci and Lucas Numbers and The Golden Section, Chichester, Ellis Horwood Limited Publ., 1989.