N-th root

TL;DR

This paper presents a method to solve quaternion equations of the form X^n=A for any integer n > 1 by leveraging the isomorphism between quaternions and (4,4)-matrices.

Contribution

It introduces a novel approach using matrix isomorphism to find solutions to quaternion nth root equations for any integer n > 1.

Findings

Successfully solves quaternion nth root equations for any integer n > 1

Utilizes quaternion-matrix isomorphism to facilitate solutions

Provides a systematic method applicable to complex quaternion elements

Abstract

The quaternion equation X^n=A is solved for any integer number n > 1. A is a given quaternion with komplex numbers as its elements. We use the isomorphism between quaternions and (4,4)-matrices to solve this equation.