Quaternions and some applications of quaternionic functions

This thesis consists of five chapters. In the first part, some basic concepts about quaternions and quaternion matrices used in this thesis are given. In the second part, polar form is explained with the help of real quaternions Cayley-Dickson form; also, the polar forms for dual, split and dual split quaternions are given with the help of the Cayley-Dickson form. In the third chapter, modeling of a triangle with the help of real quaternions is given. Then, the modeling of a spherical triangle with the help of dual quaternions are given. In addition, the modeling of Lorentz and hyperbolic triangles with the help of the split quaternions are given. In the fourth chapter, matrix representation of split quaternionic functions and their partial derivatives are given and the gradient of split quaternionic functions with the help of these are given. In the fifth chapter, the last part of the thesis, line symmetric motion in Minkowski 3-space is given,which is similar to the line symmetric motion in Euclidean space.