Fibonacci Matrisinin Kökleri Aracılığıyla Fibonacci Ve Lucas Sayılarının Özellikleri Üzerine

Bu çalışmada, ve formlarındaki rasyonel indisli kompleks Fibonacci ve Lucas sayıları için bazı eşitlikler oluşturmak için matris teorisinden genel tekniklerden faydalanırız. Bu amaçla, tek ntam sayıları için mertebeden Fibonacci matrisinin and matris fonksiyonlarını kurar ve sırasıyla and iki özel matris fonksiyonu arasındaki bazı ilişkileri ele alırız. Sırasıyla, tek n tam sayıları ve için ve formlarındaki rasyonel indisli kompleks Fibonacci ve Lucas sayıları ile ilgili bazı eşitlikler veririz.

Anahtar Kelimeler:

Fibonacci dizileri, Matris fonksiyonları, Kök matrisleri

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.

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