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The η-anti-Hermitian solution to some classic matrix equations

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  • Liu, Xin

Abstract

We in this paper consider the η-anti-Hermitian solution to some classic matrix equations AX=B,AXB=C,AXAη*=B,EXEη*+FYFη*=H, respectively. We derive the necessary and sufficient conditions for the above matrix equations to have η-anti-Hermitian solutions and also provide the general expressions of solutions when those equations are solvable. As applications, for instance, we give the solvability conditions and general η-anti-Hermitian solution to equation system AX=B,CY=D,MXMη*+NYNη*=G.

Suggested Citation

  • Liu, Xin, 2018. "The η-anti-Hermitian solution to some classic matrix equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 264-270.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:264-270
    DOI: 10.1016/j.amc.2017.09.033
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    References listed on IDEAS

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    1. 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.
    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.
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    Cited by:

    1. Long-Sheng Liu & Qing-Wen Wang & Mahmoud Saad Mehany, 2022. "A Sylvester-Type Matrix Equation over the Hamilton Quaternions with an Application," Mathematics, MDPI, vol. 10(10), pages 1-20, May.

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