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.b170765
Published online 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
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