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A System of Sylvester-type Quaternion Matrix Equations with Ten Variables

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Abstract

This paper studies a system of three Sylvester-type quaternion matrix equations with ten variables \({A_i}{X_i} + {Y_i}{B_i} + {C_i}{Z_i}{D_i} + {F_i}{Z_{i + 1}}{G_i} = {E_i},\,\,\,i = \overline {1,3} \). We derive some necessary and sufficient conditions for the existence of a solution to this system in terms of ranks and Moore-Penrose inverses of the matrices involved. We present the general solution to the system when the solvability conditions are satisfied. As applications of this system, we provide some solvability conditions and general solutions to some systems of quaternion matrix equations involving ϕ-Hermicity. Moreover, we give some numerical examples to illustrate our results. The findings of this paper extend some known results in the literature.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China

    Meng Yan Xie, Qing Wen Wang, Zhuo Heng He & Mehany Mahmoud Saad

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  1. Meng Yan Xie
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  2. Qing Wen Wang
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  3. Zhuo Heng He
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Correspondence to Qing Wen Wang.

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Supported by the National Natural Science Foundation of China (Grant No. 11971294)

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Xie, M.Y., Wang, Q.W., He, Z.H. et al. A System of Sylvester-type Quaternion Matrix Equations with Ten Variables. Acta. Math. Sin.-English Ser. 38, 1399–1420 (2022). https://doi.org/10.1007/s10114-022-9040-1

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