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Determinantal Representations of General and (Skew‐)Hermitian Solutions to the Generalized Sylvester‐Type Quaternion Matrix Equation

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  • Ivan I. Kyrchei

Abstract

In this paper, we derive explicit determinantal representation formulas of general, Hermitian, and skew‐Hermitian solutions to the generalized Sylvester matrix equation involving ⁎‐Hermicity AXA⁎ + BYB⁎ = C over the quaternion skew field within the framework of the theory of noncommutative column‐row determinants.

Suggested Citation

  • Ivan I. Kyrchei, 2019. "Determinantal Representations of General and (Skew‐)Hermitian Solutions to the Generalized Sylvester‐Type Quaternion Matrix Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2019(1).
    • Handle: RePEc:wly:jnlaaa:v:2019:y:2019:i:1:n:5926832
    DOI: 10.1155/2019/5926832
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    References listed on IDEAS

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    1. Yong Lin & Qing-Wen Wang, 2013. "Iterative Solution to a System of Matrix Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, October.
    2. Zhang, Xiang, 2016. "A system of generalized Sylvester quaternion matrix equations and its applications," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 74-81.
    3. 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.
    4. Rehman, Abdur & Wang, Qing-Wen & He, Zhuo-Heng, 2015. "Solution to a system of real quaternion matrix equations encompassing η-Hermicity," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 945-957.
    5. Feng Yin & Guang-Xin Huang, 2012. "An Iterative Algorithm for the Least Squares Generalized Reflexive Solutions of the Matrix Equations AXB = E,CXD = F," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Yong Lin & Qing-Wen Wang, 2013. "Iterative Solution to a System of Matrix Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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