Abstract
Unlike quaternions and split quaternions, reduced biquaternions satisfy the multiplication commutative rule and are commonly used in image processing, fuzzy recognition, image compression, Hopfield neural networks, and digital signal processing. However, although algebraic techniques have been developed for the diagonalisation of quaternion and split quaternion matrices, the diagonalisation of a reduced biquaternion matrix is yet to be studied. In this study, we derive sufficient and necessary conditions for the diagonalisation of a reduced biquaternion matrix and devise two numerical methods for the diagonalisation of a reduced biquaternion matrix. These methods were derived using complex and real representations in the reduced biquaternionic algebra.
Acknowledgements
The authors are grateful to the referees for their valuable comments and suggestions, which helped improve the quality of this manuscript.
Disclosure statement
The authors report there are no competing interests to declare.
Correction Statement
This article has been corrected with minor changes. These changes do not impact the academic content of the article.