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.