ON THE EIGENVALUES OF SOME TRIDIAGONAL MATRICES

---

Thesis Type: Postgraduate

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

Approval Date: 2009

Thesis Language: Turkish

Student: Simge ODABAŞ

Supervisor: DURSUN TAŞCI

Abstract:

In this study, by describing characteristic properties of Fibonacci and Lucas numbers Binet formulas of these numbers are examined with the help of recurrence relations. Additionally, the first and the second type of Chebyshev polynomials are some examined. Complex factorizations of Fibonacci and Lucas numbers are indicated. The relation between the determinants of obtained matrices in the end of this factorization and the first and the second type of Chebyshev polynomials are studied. The eigenvalues and inverse of some tridiagonal matrices are given. Finally, it is examined that relation between eigenvalues of the tridiagonal matrices and the second type of Chebyshev polynomials are given. Science Code : 204.1.025 Key Words : Fibonacci, Lucas numbers, Chebyshev polynomials, Binet formula and tridioganal matrices,eigenvalues