Turkish Journal of Mathematics
Abstract
Quaternions have become a popular and powerful tool in various engineering fields, such as robotics, image and signal processing, and computer graphics. However, classical quaternions are mostly used as a representation of rotation of a vector in $3$-dimensions, and connection between its geometric interpretation and algebraic structures is still not well-developed and needs more improvements. In this study, we develop an approach to understand quaternions multiplication defining subspaces of quaternion $\mathbb{H}$, called as $\mbox{Plane}(N)$ and $\mbox{Line}(N)$, and then, we observe the effects of sandwiching maps on the elements of these subspaces. Finally, we give representations of some transformations in geometry using quaternion.
DOI
10.3906/mat-1907-120
Keywords
Quaternions, reflection, orthogonal projection, sandwiching maps, involution and antiinvolution
First Page
1289
Last Page
1303
Recommended Citation
DEMİRCİ, B. B, & AGHAYEV, N (2020). On geometric applications of quaternions. Turkish Journal of Mathematics 44 (4): 1289-1303. https://doi.org/10.3906/mat-1907-120
