Algebraic algorithms for eigen-problems of a reduced biquaternion matrix and applications

Zhenwei Guo, Tongsong Jiang, Gang Wang and V.I. Vasil'ev

Applied Mathematics and Computation, 2024, vol. 463, issue C

Abstract: In recent years, the reduced biquaternion algebras have been widely used in color image processing problems and in the field of electromagnetism. This paper studies eigen-problems of reduced biquaternion matrices by means of a complex representation of a reduced biquaternion matrix and derives new algebraic algorithms to find the eigenvalues and eigenvectors of reduced biquaternion matrices. This paper also concludes that the number of eigenvalues of an n×n reduced biquaternion matrix is infinite. In addition, the proposed algebraic algorithms are shown to be effective in application to a color face recognition problem.

Keywords: Reduced biquaternion matrix; Complex representation; Eigenvalue; Eigenvector; Algebraic algorithm (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:463:y:2024:i:c:s0096300323005271

DOI: 10.1016/j.amc.2023.128358

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