Commutative Quaternion Matrices

TL;DR

This paper introduces the concept of commutative quaternion matrices, explores their properties, and establishes their relationship with complex matrices, providing foundational insights into their algebraic structure.

Contribution

It defines commutative quaternion matrices, investigates their properties, and introduces the complex adjoint matrix, expanding the understanding of quaternion algebra.

Findings

Properties of commutative quaternions and Hamilton matrices

Definition and properties of the complex adjoint matrix

Relationship between commutative quaternion matrices and complex matrices

Abstract

In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative quaternion matrices using properties of complex matrices. Then we define the complex adjoint matrix of commutative quaternion matrices and give some of their properties.