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Cramer’s rule for a system of quaternion matrix equations with applications

Author

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  • Song, Guang-Jing
  • Wang, Qing-Wen
  • Yu, Shao-Wen

Abstract

In this paper, we investigate Cramer’s rule for the general solution to the system of quaternion matrix equations A1XB1=C1,A2XB2=C2,and Cramer’s rule for the general solution to the generalized Sylvester quaternion matrix equation AXB+CYD=E,respectively. As applications, we derive the determinantal expressions for the Hermitian solutions to some quaternion matrix equations. The findings of this paper extend some known results in the literature.

Suggested Citation

  • Song, Guang-Jing & Wang, Qing-Wen & Yu, Shao-Wen, 2018. "Cramer’s rule for a system of quaternion matrix equations with applications," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 490-499.
    • Handle: RePEc:eee:apmaco:v:336:y:2018:i:c:p:490-499
    DOI: 10.1016/j.amc.2018.04.056
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    Cited by:

    1. Emad E. Mahmoud & M. Higazy & Turkiah M. Al-Harthi, 2019. "A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Applicatio," Mathematics, MDPI, vol. 7(10), pages 1-26, September.
    2. Mahmoud, Emad E. & Higazy, M. & Alotaibi, Hammad & Abo-Dahab, S.M. & Abdel-Khalek, S. & Khalil, E.M., 2021. "Quaternion anti-synchronization of a novel realizable fractional chaotic model," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    3. Tan, Manchun & Liu, Yunfeng & Xu, Desheng, 2019. "Multistability analysis of delayed quaternion-valued neural networks with nonmonotonic piecewise nonlinear activation functions," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 229-255.
    4. Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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