Conference Paper

Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product

Volume: 3 Number: 1 December 15, 2020
Conference Proceedings of Science and Technology Cover
Conference Proceedings of Science and Technology
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Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product

Abstract

The Fibonacci number sequence and related calculations come up in scientific facts in many events we encounter in daily life. This special number sequence is processed in the occurrence of many events such as calculating the diameter of the equatorial circumference of the Earth, flowers, growth and structures of leaves, trees, reproduction of bees, sunflower and so on. [6]. However, in recent years, the relation between the Fibonacci and Lucas Number sequences with continued fractions and matrices has intensively been studied. Many identities have been found by some 2X2 types of special matrices with nth power that have been associated with the Fibonacci and Lucas numbers. The aim of this study is to examine matrix (1 1 -1 0) under the lorentzian matrix product with nth power, quadratic equations and characteristic roots unlike the classical matrix product. In addition, we want to acquire some identities with the help of matrix (1 1 -1 0) under the lorentzian matrix product with nth power in relation to the Fibonacci and Lucas numbers.

Keywords

References

  1. 1 B.U. Alfred, An Introduction to Fibonacci Discovery, The Fibonacci Association, (1965).
  2. 2 C.K. Ho, H.S. Woon and C-Y. Chong, Generating Matrix and Sums of Fibonacci and Pell Sequences , AIP Conference Proceedings, 1605,( 2014) 678.
  3. 3 H. Gundogan and O. Kecilioglu, Lorentzian Matrix Multiplication and the Motions on Lorentzian Plane, Glasnik Matematicki, Vol. (41)61, (2006), 329-334.
  4. 4 M.Bicknell and V. E. Hoggatt, A Primer for the Fibonacci Numbers: Part XIV, The Fibonacci Quarterly, 12:2 (April), (1974),147-156.
  5. 5 S. Falcon, Relationships Between Some k-Fibonacci Sequences, Appl. Math., 5,( 2014), 2226-2234.
  6. 6 T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, New York, Toronto, (2001).
  7. 7 V.E. Hoggatt,Fibonacci and Lucas Numbers, The Fibonacci Association, Santa Clara (1969).

Details

Primary Language

English

Subjects

Engineering

Journal Section

Conference Paper

Authors

Publication Date

December 15, 2020

Submission Date

July 24, 2020

Acceptance Date

September 30, 2020

Published in Issue

Year 1970 Volume: 3 Number: 1

IZ

https://izlik.org/JA35XF74UN

Cite

RIS / Bibtex
APA
Gökcan, İ., & Değer, A. H. (2020). Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology, 3(1), 102-109. https://izlik.org/JA35XF74UN
AMA
1.Gökcan İ, Değer AH. Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology. 2020;3(1):102-109. https://izlik.org/JA35XF74UN
Chicago
Gökcan, İbrahim, and Ali Hikmet Değer. 2020. “Obtaining Some Identities With the Nth Power of a Matrix Under the Lorentzian Product”. Conference Proceedings of Science and Technology 3 (1): 102-9. https://izlik.org/JA35XF74UN.
EndNote
Gökcan İ, Değer AH (December 1, 2020) Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology 3 1 102–109.
IEEE
[1]İ. Gökcan and A. H. Değer, “Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product”, Conference Proceedings of Science and Technology, vol. 3, no. 1, pp. 102–109, Dec. 2020, [Online]. Available: https://izlik.org/JA35XF74UN
ISNAD
Gökcan, İbrahim - Değer, Ali Hikmet. “Obtaining Some Identities With the Nth Power of a Matrix Under the Lorentzian Product”. Conference Proceedings of Science and Technology 3/1 (December 1, 2020): 102-109. https://izlik.org/JA35XF74UN.
JAMA
1.Gökcan İ, Değer AH. Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology. 2020;3:102–109.
MLA
Gökcan, İbrahim, and Ali Hikmet Değer. “Obtaining Some Identities With the Nth Power of a Matrix Under the Lorentzian Product”. Conference Proceedings of Science and Technology, vol. 3, no. 1, Dec. 2020, pp. 102-9, https://izlik.org/JA35XF74UN.
Vancouver
1.İbrahim Gökcan, Ali Hikmet Değer. Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology [Internet]. 2020 Dec. 1;3(1):102-9. Available from: https://izlik.org/JA35XF74UN