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, BURCU BEKTAŞ and AGHAYEV, NAZIM
(2020)
"On geometric applications of quaternions,"
Turkish Journal of Mathematics: Vol. 44:
No.
4, Article 15.
https://doi.org/10.3906/mat-1907-120
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss4/15
