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

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 a...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 463; p. 128358
Main Authors: Guo, Zhenwei, Jiang, Tongsong, Wang, Gang, Vasil'ev, V.I.
Format: Journal Article
Language:English
Published: Elsevier Inc 15.02.2024
Subjects:
Algebraic algorithm
Complex representation
Eigenvalue
Eigenvector
Reduced biquaternion matrix
Eigenvalue
Reduced biquaternion matrix
Eigenvector
Algebraic algorithm
Complex representation
ISSN:0096-3003
Online Access:Get full text
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Summary: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. •The eigen-problems of reduced biquaternion matrices are further studied based on the complex representation form.•Propose new algebraic algorithms for finding the eigenvalues and the eigenvectors of a reduced biquaternion matrix.•An n×n reduced biquaternion matrix has infinite eigenvalues.•There are multiple eigenvalues corresponding to the same eigenvector of a reduced biquaternion matrix.•The proposed method is more comprehensive and can find more eigenvalues of a reduced biquaternion matrix.
ISSN:0096-3003
DOI:10.1016/j.amc.2023.128358