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Determinantal representation of the generalized inverses over the quaternion skew field with applications. (English) Zbl 1302.15007

Summary: We establish some new determinantal representations of the generalized inverses \(A_{r_{T_1,S_1}}^{(2)}\), \(A_{r_{T_2,S_2}}^{(2)}\) and \(A_{(T_1,T_2),(S_1,S_2)}^{(2)}\) over the quaternion skew field by the theory of the column and row determinants. In addition, we derive a condensed Cramer rule for the unique solution of some restricted quaternion matrix equations. The findings of this paper extend some known results in the literature.

MSC:

15A09 Theory of matrix inversion and generalized inverses
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