Akademik Veri Yönetim Sistemi
Tez Türü: Yüksek Lisans
Tezin Yürütüldüğü Kurum: Akdeniz Üniversitesi, Fen Bilimleri Enstitüsü, Matematik, Türkiye
Tez Danışmanı: Özdemir M.
Tezin Onay Tarihi: 2017
Desteklendiği Program: Bu tezi destekleyen bir program bulunmamaktadır
Özet:
In this study, hyperbolic numbers and whose entries are hyperbolic numbers are investigated. Numbers are firstly introduced generalized complex numbers are introduced and basic operations on hyperbolic numbers, a special subset of generalized complex numbers, are examined. Polar, exponential and matrix forms of a hyperbolic number are represented with respect to characterization of hyperbolic number. Also, the roots of a timelike, spacelike or null hyperbolic number are expressed, using De Moivre formula given for hyperbolic numbers. Moreover, some algebraic properties of hyperbolic numbers are studied in the Lorentzian plane. In the later parts of the thesis, hermitian scalar product and hermitian cross product are given by using the hyperbolic vector notion. Also, hyperbolic unitary matrices are defined and obtained with different methods. At last, some algebraic properties of exponential of matrices with hyperbolic numbers are studied.