Universal similarity factorization equalities for commutative quaternions and their matrices

ABSTRACT

In this work, we have established universal similarity factorization equalities over the commutative quaternions and their matrices. Based on these equalities, real matrix representations of commutative quaternions and their matrices have been derived, and their algebraic properties and fundamental equations have been determined. Moreover, illustrative examples are provided to support our results.

KEYWORDS:

• Commutative quaternions and their matrices
• real matrix representations
• universal similarity factorization equality

AMS SUBJECT CLASSIFICATIONS:

• 15A18
• 15B33

Acknowledgements

The authors would like to thank the anonymous referees for their helpful suggestions and comments which improved significantly the presentation of the paper.

Notes

No potential conflict of interest was reported by the authors.