ON THE FIBONACCI SEQUENCE AND HESSENBERG MATRICES

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Thesis Type: Postgraduate

Institution Of The Thesis: Gazi University, Fen Bilimleri Enstitüsü, Turkey

Approval Date: 2009

Thesis Language: Turkish

Student: Huriye AZMAN

Supervisor: DURSUN TAŞCI

Abstract:

In this study, by describing properties characteristic of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal and Jacobsthal-Lucas sequences; Binet formulas of these sequences are examined with the help of reccurence relations. Additionally, generating matrices of Fibonacci sequence are mentioned. Some identities about of Fibonacci and Lucas numbers are obtained. Some n×n matrices are given whose determinats obtain Fibonacci numbers. Five new classes of Fibonacci- Hessenberg matrices are introduced and the definition of two-dimensional Fibonacci arrays are given. Finally, linear equations are given whose solutions are Fibonacci fractions.