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 Determinantal expression of the general solution to a restricted system of quaternion matrix equations with applications Bull. Korean Math. Soc. 2018 Vol. 55, No. 4, 1285-1301 https://doi.org/10.4134/BKMS.b170765Published online June 11, 2018Printed July 31, 2018 Guang-Jing Song Weifang University Abstract : In this paper, we mainly consider the determinantal representations of the unique solution and the general solution to the restricted system of quaternion matrix equations $\left\{ \begin{array} [c]{c} A_{1}X=C_{1}\\ XB_{2}=C_{2}, \end{array} \right. \mathcal{R}_{r}\left( X\right) \subseteq T_{1},\text{ } \mathcal{N}_{r}\left( X\right) \supseteq S_{1},$ respectively. As an application, we show the determinantal representations of the general solution to the restricted quaternion matrix equation $AX+YB=E,\text{ }\mathcal{R}_{r}\left( X\right) \subseteq T_{1},\text{ }\mathcal{N}_{r}\left( X\right) \supseteq S_{1},\text{ }\mathcal{R} _{l}\left( Y\right) \subseteq T_{2},\text{ }\mathcal{N}_{l}\left( Y\right) \supseteq S_{2}.$ The findings of this paper extend some known results in the literature. Keywords : quaternion matrix, Cramer's rule, determinant MSC numbers : 15A09, 15A24 Downloads: Full-text PDF