Some Properties of 3x3 Octonionic Hermitian Matrices with Non-Real Eigenvalues

TL;DR

This paper explores the properties of 3x3 Hermitian matrices over octonions, focusing on their eigenvalues, extending prior work on smaller matrices to understand their spectral characteristics.

Contribution

It introduces the initial investigation into 3x3 octonionic Hermitian matrices with non-real eigenvalues, expanding the understanding from 2x2 cases.

Findings

Preliminary analysis of eigenvalue properties

Extension of 2x2 results to 3x3 matrices

Identification of challenges in octonionic spectral theory

Abstract

We discuss our preliminary attempts to extend previous work on 2x2 Hermitian octonionic matrices with non-real eigenvalues to the 3x3 case.