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On the general solutions to some systems of quaternion matrix equations

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

In this paper, we consider a system of three coupled quaternion matrix equations \(A_{i}X_{i}+Y_{i}B_{i}+C_{i}ZD_{i}=E_{i}\), where \(A_{i},B_{i},C_{i},D_{i},\) and \(E_{i}\) are given matrices, \(X_{i},Y_{i},\) and Z are unknowns \((i=1,2,3)\). We establish some practical necessary and sufficient conditions for the existence of a solution to this system, and present the general solution to the system. As applications of this system, we give some solvability conditions and general solutions to some systems of quaternion matrix equations involving \(\eta \)-Hermicity. Some examples are given to illustrate the main results. Some of the findings of this paper extend some known results in the literature.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, People’s Republic of China

    Zhuo-Heng He & Meng Wang

  2. Faculty of Information Technology, Macau University of Science and Technology, Avenida Wai Long, TaiPa, Macau, 999078, People’s Republic of China

    Xin Liu

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  1. Zhuo-Heng He
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  2. Meng Wang
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  3. Xin Liu
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Correspondence to Xin Liu.

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This research was supported by the National Natural Science Foundation of China (Grant nos. 11801354 and 11971294), The Science and Technology Development Fund, Macau SAR (File no. 185/2017/A3), National Natural Science Foundation for the Youth of China (Grant no. 11701598)

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He, ZH., Wang, M. & Liu, X. On the general solutions to some systems of quaternion matrix equations. RACSAM 114, 95 (2020). https://doi.org/10.1007/s13398-020-00826-2

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