Obtaining Some Identities with the 𝒏th Power of Matrix ( 𝟏 𝟏 −𝟏 𝟎 ) Under The Lorentzian Product


Gökcan İ., Değer A. H.

3rd INTERNATIONAL E-CONFERENCE ON MATHEMATICAL ADVANCES AND ITS APPLICATIONS, İstanbul, Turkey, 24 - 27 June 2020, pp.107

  • Publication Type: Conference Paper / Summary Text
  • City: İstanbul
  • Country: Turkey
  • Page Numbers: pp.107

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. (Koshy, 2001).
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 2 × 2 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)  under the lorentzian
matrix product with nth  power, quadratic equations and characteristic
−1     0
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: Fibonacci and Lucas Numbers, Lorentzian Matrix Multiplication, Quadratic Equation,
Characteristic Root.