Cramer rule for the unique solution of restricted matrix equations over the quaternion skew field

摘要

In this paper, we establish the determinantal representations of the generalized inverses A~((2))_(rr1,s1) and A~((2))_((T_1,T_2),(S_1,S_2)) over the quaternion skew field by the theory of the column and row determinants. In addition, we derive some generalized Cramer rules for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature.