# Quaternionic left eigenvalue problem: a matrix representation

## TL;DR

This paper introduces a new methodology and tools for computing the left eigenvalues of quaternion matrices by solving specific polynomial equations, and explores their properties.

## Contribution

It provides a novel approach with a matrix representation to find quaternionic left eigenvalues, including solving polynomial equations and analyzing their properties.

## Key findings

- Developed tools for eigenvalue computation of quaternion matrices
- Reduced the problem to solving polynomial equations of degree up to 4m-3
- Investigated properties of quaternionic left eigenvalues

## Abstract

This paper presents an innovative set of tools developed to support a methodology to find the left eigenvalues of $m$ order quaternion square matrix. It is solving four real polynomial equations of order not greater than $4m-3$ in four variables. Some important properties of these eigenvalues are also investigated.