Bott-Duffin inverse over the quaternion skew field with applications

In this paper, we show some properties of the Bott-Duffin inverses $A_{r_{ ( L_{1} ) }}^{ ( -1 ) }$ and $A_{l_{ ( L_{2} ) }}^{ ( -1 ) }$ over the quaternion skew field. In particular, we establish the determinantal representations of these generalized inverses by the theory of the column and row determinants. Moreover, we derive some Cramer rules for the unique solution to some restricted linear quaternion equations. The findings of this paper extend some known results in the literature.