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Algebraic techniques for Maxwell’s equations in commutative quaternionic electromagnetics

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Abstract

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 \(\Vert A\alpha -\alpha \lambda \Vert _F=\min \) 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.

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Authors and Affiliations

  1. Institute of Mathematics and Information Science, North-Eastern Federal University, Yakutsk, Russia, 677000

    Zhenwei Guo, Dong Zhang, Vasily. I. Vasiliev & Tongsong Jiang

  2. School of Mathematics and Statistics, Linyi University, Linyi, 276005, Shandong, People’s Republic of China

    Tongsong Jiang

  3. School of Mathematics and Statistics, Heze University, Heze, 274015, Shandong, People’s Republic of China

    Zhenwei Guo, Dong Zhang & Tongsong Jiang

Authors
  1. Zhenwei Guo
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  2. Dong Zhang
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  3. Vasily. I. Vasiliev
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  4. Tongsong Jiang
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Corresponding authors

Correspondence to Vasily. I. Vasiliev or Tongsong Jiang.

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This work does not have any conflicts of interest.

Additional information

This paper is supported by the Shandong Natural Science Foundation (ZR201709250116) and Chinese Government Scholarship (CSC NO. 202108370087, CSC NO. 202108370086)

The original online version of this article was revised to amend the order of author names in the xml to Zhenwei Guo, Dong Zhang, Vasily. I. Vasiliev, Tongsong Jiang.

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Guo, Z., Zhang, D., Vasiliev, V.I. et al. Algebraic techniques for Maxwell’s equations in commutative quaternionic electromagnetics. Eur. Phys. J. Plus 137, 577 (2022). https://doi.org/10.1140/epjp/s13360-022-02794-5

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  • DOI: https://doi.org/10.1140/epjp/s13360-022-02794-5

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