Matrix Theory over the Complex Quaternion Algebra

TL;DR

This paper develops foundational matrix analysis tools over the complex quaternion algebra, including generalized inverses, eigenvalues, eigenvectors, similarity, and determinants, to advance mathematical understanding in this area.

Contribution

It introduces fundamental tools for matrix analysis over complex quaternions, enabling further research and applications in this mathematical domain.

Findings

Development of generalized inverses for complex quaternion matrices

Analysis of eigenvalues and eigenvectors in complex quaternion matrices

Formulation of determinants and similarity transformations for complex quaternion matrices

Abstract

We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex quaternion matrices, and so on.