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 June 11, 2018 Printed 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.