On geometric applications of quaternions

Abstract

Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, imageand signal processing, and computer graphics. However, classical quaternions are mostly used as a representation ofrotation of a vector in 3-dimensions, and connection between its geometric interpretation and algebraic structures isstill not well-developed and needs more improvements. In this study, we develop an approach to understand quaternionsmultiplication defining subspaces of quaternion H, called as Plane(N) and Line(N), and then, we observe the effectsof sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations ingeometry using quaternion.