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Solution to a system of real quaternion matrix equations encompassing η-Hermicity

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  • Rehman, Abdur
  • Wang, Qing-Wen
  • He, Zhuo-Heng

Abstract

Let Hm×n be the set of all m × n matrices over the real quaternion algebra H={c0+c1i+c2j+c3k∣i2=j2=k2=ijk=−1,c0,c1,c2,c3∈R}. A∈Hn×n is known to be η-Hermitian if A=Aη*=−ηA*η,η∈{i,j,k} and A* means the conjugate transpose of A. We mention some necessary and sufficient conditions for the existence of the solution to the system of real quaternion matrix equations including η-Hermicity A1X=C1,A2Y=C2,YB2=D2,Y=Yη*,A3Z=C3,ZB3=D3,Z=Zη*,A4X+(A4X)η*+B4YB4η*+C4ZC4η*=D4,and also construct the general solution to the system when it is consistent. The outcome of this paper diversifies some particular results in the literature. Furthermore, we constitute an algorithm and a numerical example to comprehend the approach established in this treatise.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:945-957
    DOI: 10.1016/j.amc.2015.05.104
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    Cited by:

    1. Kyrchei, Ivan, 2017. "Weighted singular value decomposition and determinantal representations of the quaternion weighted Moore–Penrose inverse," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 1-16.
    2. Liu, Xin, 2018. "The η-anti-Hermitian solution to some classic matrix equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 264-270.
    3. Rehman, Abdur & Wang, Qing-Wen, 2015. "A system of matrix equations with five variables," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 805-819.

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