Split Quaternion Matrix Representation of Dual Split Quaternions and Their Matrices

In this paper, we present some important properties of matrices over dual split quaternions. We examine dual split quaternion matrices by their split quaternion matrix representation. Then, we give some interesting results for 2 × 2 split quaternion matrix representation of a dual split quaternion. Finally, we prove that the group HD\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{H}_{\mathbb{D}}}$$\end{document} and SC(2,H^)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${SC(2, \widehat{\mathbb{H}})}$$\end{document} are isomorphic.