Some remarks regarding Quaternions and Octonions

TL;DR

This paper explores applications of quaternions and octonions, providing matrix representations and properties useful for computations, along with identifying invertible elements in split quaternion and octonion algebras.

Contribution

It introduces real matrix representations for complex octonions and characterizes invertible elements in split quaternion and octonion algebras, advancing computational methods.

Findings

Matrix representations for complex octonions are established.

A set of invertible elements in split quaternion and octonion algebras is identified.

Properties of these algebraic structures are analyzed for computational applications.

Abstract

In this paper, we present some applications of quaternions and octonions. We present the real matrix representations for complex octonions and some of their properties which can be used in computations where these elements are involved. Moreover, we give a set of invertible elements in split quaternion algebras and in split octonion algebras.