On geometric applications of quaternions

Abstract

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