On quaternions of special number sequences

In this thesis a detailed study is made about the quaternions of special number sequences. Especially Tribonacci quaternions and Tribonacci-Lucas quaternions are examined in detail and fundamental identities are reproved again by using a different Fibonacci quaternion matrix. This thesis consists of seven sections. In the first section, a detailed literature review of the subject is given. In the second section, the concepts and theorems used throughout the thesis are given as fundamental information. In the third section, quaternions and their fundamental properties are given. In the fourth section, quaternions and properties of special number sequences such as Fibonacci and Lucas are studied in detail. In the fifth section, the quaternions of Tribonacci and Tribonacci-Lucas number sequences are given and some identities of Tribonacci and Tribonacci-Lucas quaternions are proved. In the sixth section, some known fundamental identities such as Cassini identity for Fibonacci and Lucas quaternions are reproved by using a different Fibonacci quaternion matrix. In the Conclusion and Suggestions section, after giving a brief summary of the study, the contribution of the thesis to the literature and some suggestions for future studies are presented.