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

Year 2020, Volume: 3 Issue: 1, 102 - 109, 15.12.2020

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.

References

  • 1 B.U. Alfred, An Introduction to Fibonacci Discovery, The Fibonacci Association, (1965).
  • 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 H. Gundogan and O. Kecilioglu, Lorentzian Matrix Multiplication and the Motions on Lorentzian Plane, Glasnik Matematicki, Vol. (41)61, (2006), 329-334.
  • 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 S. Falcon, Relationships Between Some k-Fibonacci Sequences, Appl. Math., 5,( 2014), 2226-2234.
  • 6 T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, New York, Toronto, (2001).
  • 7 V.E. Hoggatt,Fibonacci and Lucas Numbers, The Fibonacci Association, Santa Clara (1969).
Year 2020, Volume: 3 Issue: 1, 102 - 109, 15.12.2020

Abstract

References

  • 1 B.U. Alfred, An Introduction to Fibonacci Discovery, The Fibonacci Association, (1965).
  • 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 H. Gundogan and O. Kecilioglu, Lorentzian Matrix Multiplication and the Motions on Lorentzian Plane, Glasnik Matematicki, Vol. (41)61, (2006), 329-334.
  • 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 S. Falcon, Relationships Between Some k-Fibonacci Sequences, Appl. Math., 5,( 2014), 2226-2234.
  • 6 T. Koshy, Fibonacci and Lucas Numbers with Applications, John Wiley and Sons, New York, Toronto, (2001).
  • 7 V.E. Hoggatt,Fibonacci and Lucas Numbers, The Fibonacci Association, Santa Clara (1969).
There are 7 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

İbrahim Gökcan 0000-0002-6933-8494

Ali Hikmet Değer 0000-0003-0764-715X

Publication Date December 15, 2020
Acceptance Date September 30, 2020
Published in Issue Year 2020 Volume: 3 Issue: 1

Cite

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.
AMA Gökcan İ, Değer AH. Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product. Conference Proceedings of Science and Technology. December 2020;3(1):102-109.
Chicago 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 3, no. 1 (December 2020): 102-9.
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 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, 2020.
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 2020), 102-109.
JAMA 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, 2020, pp. 102-9.
Vancouver 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):102-9.