Fibonacci Matrisinin Kökleri Aracılığıyla Fibonacci Ve Lucas Sayılarının Özellikleri Üzerine

Abstract

In this study, we exploit general techniques from matrix theory to establish some identities for the complex Fibonacci and Lucas numbers with rational subscripts of the forms 2 n and ns. For this purpose, we establish matrix functions 2 n RR → and ns RR → of the Fibonacci matrix R of order 33  for integer odd n and discuss some relations between two special matrices functions 2 n R and ns R , respectively. Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms 2 n and ns are given for every integer odd n and