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\(\eta \)-Hermitian Solution to a System of Quaternion Matrix Equations

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Abstract

For \(\eta \in \{{\mathbf {i}},{\mathbf {j}},{\mathbf {k}}\}\), a real quaternion matrix A is said to be \(\eta \)-Hermitian if \(A=A^{\eta *},\) where \(A^{\eta *}=-\eta A^{*}\eta \), and \(A^{*}\) stands for the conjugate transpose of A. In this paper, we present some practical necessary and sufficient conditions for the existence of an \(\eta \)-Hermitian solution to a system of constrained two-sided coupled real quaternion matrix equations and provide the general \(\eta \)-Hermitian solution to the system when it is solvable. Moreover, we present an algorithm and a numerical example to illustrate our results.

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Acknowledgements

The authors thank the anonymous referees for their valuable suggestions that improved the exposition of this article.

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Authors and Affiliations

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

    Xin Liu

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

    Zhuo-Heng He

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  1. Xin Liu
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Correspondence to Zhuo-Heng He.

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Communicated by Fuad Kittaneh.

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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 (Grant No. 185/2017/A3), and National Natural Science Foundation for the Youth of China (Grant No. 11701598).

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Liu, X., He, ZH. \(\eta \)-Hermitian Solution to a System of Quaternion Matrix Equations. Bull. Malays. Math. Sci. Soc. 43, 4007–4027 (2020). https://doi.org/10.1007/s40840-020-00907-w

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  • DOI: https://doi.org/10.1007/s40840-020-00907-w

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