De- Moivre's and Euler Formulas for Matrices of Split Quaternions

TL;DR

This paper explores matrix representations of split quaternions, deriving De-Moivre's and Euler's formulas for these matrices, distinguishing between timelike, spacelike, and pure split quaternions.

Contribution

It introduces De-Moivre's and Euler's formulas specifically for real matrices of split quaternions, expanding the mathematical framework for these hypercomplex numbers.

Findings

De-Moivre's formula derived for timelike split quaternions

De-Moivre's formula derived for spacelike split quaternions

Euler theorem established for pure split quaternions

Abstract

In this paper, real matrix representations of split quaternions are examined in terms of the casual character of quaternion. Then, we give De-Moivre' s formula for real matrices of timelike and spacelike split quaternions, separately. Finally, we state the Euler theorem for real matrices of pure split quaternions.