Algebraic techniques for Maxwell’s equations in commutative quaternionic electromagnetics

The Maxwell’s equations of commutative quaternions play an important role in commutative quaternion electromagnetism. This paper studies the problem of solutions to Maxwell’s equations of commutative quaternions by means of a real representation of commutative quaternion matrices. This paper first d...

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Bibliographic Details
Published in:European physical journal plus 2022-05, Vol.137 (5), p.577, Article 577
Main Authors: Guo, Zhenwei, Zhang, Dong, Vasiliev, Vasily. I., Jiang, Tongsong
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Eigenvalues
Eigenvectors
Electromagnetism
Magnetic fields
Mathematical and Computational Physics
Maxwell's equations
Molecular
Norms
Optical and Plasma Physics
Physics
Physics and Astronomy
Quaternions
Regular Article
Representations
Theoretical
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Summary:The Maxwell’s equations of commutative quaternions play an important role in commutative quaternion electromagnetism. This paper studies the problem of solutions to Maxwell’s equations of commutative quaternions by means of a real representation of commutative quaternion matrices. This paper first derives an algebraic technique for finding solutions of the least squares eigen-problem ‖ A α - α λ ‖ F = min of the commutative quaternion matrix and also gives algebraic technique for finding the eigenvalues and corresponding eigenvectors of the commutative quaternion matrix. A numerical experiment is provided to demonstrate the feasibility of the real representation algorithm.
ISSN:2190-5444
2190-5444
DOI:10.1140/epjp/s13360-022-02794-5