3x3 Dimensional Special Matrices Associated with Fibonacci and Lucas Numbers

Year 2018, Volume: 22 Issue: 6, 1917 - 1922, 01.12.2018

Sinan Karakaya , Halim Özdemir , Tuğba Petik

https://doi.org/10.16984/saufenbilder.479060

Cited By: 1

Abstract

In the study, it has been developed a method for deriving special matrices of 3x3 dimensions, whose powers are related to Fibonacci and Lucas numbers, and some special matrices have been found via the method developed. Also, it has been given some identities related to the matrices found.

Keywords

Fibonacci numbers, Lucas numbers, Matrices

References

• [1] T. Koshy, Fibonacci and Lucas Numbers with Applications, Wiley Interscience, 2001.
• [2] R. C. Johnson, Fibonacci Numbers and Matrices, Durham University, 2009.
• [3] S. Vajda, Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications, Ellis Horwood Limited Publ., 9-62, 1989.
• [4] B. Demirtürk, Fibonacci and Lucas Sums with Matrix Method, International Mathematical Forum, 5(3), 99-107, 2010.
• [5] R. A. Dunlop, The Golden Ratio and Fibonacci Numbers, World Scientific Publishing, 35-62, 1997.
• [6] A. M. Meinke, Fibonacci Numbers and Associated Matrices, Thesis Submitted to Kent States University, 2011.
• [7] T. Mekonnen, On The Fibonnacci Numbers, Thesis Submitted to Addis Ababa University, 2013.