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

Yıl 2020, Cilt: 3 Sayı: 1, 102 - 109, 15.12.2020

İbrahim Gökcan , Ali Hikmet Değer

Öz

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.

Anahtar Kelimeler

Characteristic root Fibonacci and lucas numbers Lorentzian matrix multiplication Quadratic equation

Kaynakça

  • 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).

Yıl 2020, Cilt: 3 Sayı: 1, 102 - 109, 15.12.2020

İbrahim Gökcan , Ali Hikmet Değer

Öz

Kaynakça

  • 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).
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

İbrahim Gökcan 0000-0002-6933-8494

Ali Hikmet Değer 0000-0003-0764-715X

Yayımlanma Tarihi 15 Aralık 2020
Kabul Tarihi 30 Eylül 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 3 Sayı: 1

Kaynak Göster

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. Aralık 2020;3(1):102-109.
Chicago Gökcan, İbrahim, ve Ali Hikmet Değer. “Obtaining Some Identities With the Nth Power of a Matrix Under the Lorentzian Product”. Conference Proceedings of Science and Technology 3, sy. 1 (Aralık 2020): 102-9.
EndNote Gökcan İ, Değer AH (01 Aralık 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 ve A. H. Değer, “Obtaining Some Identities With the nth Power of a Matrix Under the Lorentzian Product”, Conference Proceedings of Science and Technology, c. 3, sy. 1, ss. 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 (Aralık 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 ve Ali Hikmet Değer. “Obtaining Some Identities With the Nth Power of a Matrix Under the Lorentzian Product”. Conference Proceedings of Science and Technology, c. 3, sy. 1, 2020, ss. 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.
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