On The Properties Of The Complex Fibonacci And Lucas Numbers With Rational Subscript Via Roots Of The Fibonacci Matrix

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 and . For this purpose, we establish matrix functions and of the Fibonacci matrix of order for integer odd nand discuss some relations between two special matrices functions and , respectively. Also, some identities related to the complex Fibonacci and Lucas numbers with rational subscripts of the forms and are given for every integer odd n and, respectively