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An algebraic algorithm for the diagonalization of a biquaternion matrix in the biquaternionic mechanics

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Abstract

Biquaternion algebra is an algebraic structure originating from a complex number and has mainly been used in quantum mechanics, special and general relativity, classical, relativistic, and covariant electrodynamics, and signal processing. In this paper, the problem of the diagonalization of a biquaternion matrix is studied, by means of a complex representation of a biquaternion matrix, and an algebraic algorithm for the diagonalization of a biquaternion matrix is presented. In addition, numerical examples demonstrate the effectiveness of the algebraic algorithm.

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Authors and Affiliations

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

    Dong Zhang, Zhenwei Guo & V. I. Vasil’ev

  2. School of Electronic Information, Shandong Xiandai University, Jinan, 250104, Shandong, People’s Republic of China

    Tongsong Jiang

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

    Tongsong Jiang

Authors
  1. Dong Zhang
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  2. Tongsong Jiang
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  3. Zhenwei Guo
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  4. V. I. Vasil’ev
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Correspondence to Tongsong Jiang or V. I. Vasil’ev.

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The research of V. I. Vasil’ev and Dong Zhang is supported by the Ministry of Science and Higher Education of the Russian Federation grant No. FSRG-2023-0025 (section 2). The research of Tongsong Jiang and Zhenwei Guo is supported by the Ministry of Science and Higher Education of the Russian Federation, agreement No. 075-02-2024-1441, February 28, 2024 (sections 3, 4). The research of Dong Zhang and Zhenwei Guo is supported by the Chinese Government Scholarship (CSC No. 202108370086, CSC No. 202108370087).

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Zhang, D., Jiang, T., Guo, Z. et al. An algebraic algorithm for the diagonalization of a biquaternion matrix in the biquaternionic mechanics. Comp. Appl. Math. 43, 221 (2024). https://doi.org/10.1007/s40314-024-02739-x

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  • DOI: https://doi.org/10.1007/s40314-024-02739-x

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