Determinantal representations of the generalized inverses A_{T,S}^{(2)} over the quaternion skew field with applications

We first present some determinantal representations of one {1,5}-inverse of a quaternion matrix within the framework of a theory of the row and column determinants. As applications, we show some new explicit expressions of generalized inverses $A_{r_{T_{1}, S_{1}}}^{( 2)}$ , $A_{l_{T_{2},S_{2}}}^{(2)}$ and $A_{_{( T_{1},T_{2}) , ( S_{1},S_{2}) }}^{( 2) }$ over the quaternion skew field. Finally, we give the representations of the unique solution to some restricted left and right systems of quaternionic linear equations. The findings of this paper extend some known results in the literature.