Abstract
The shorted operator defined by Mitra and Puri [10] and the generalized Schur complement of Ando [2] are considered for matrices over an arbitrary field F and characterized by using rank decomposition matrices. A duality between these two concepts, as well as an explicit formula for each operator, is established, and some applications to partitioned matrices are given. Moreover, we suggest an alternative definition of a shorted operator by means of generalized projections which leads, at least in the case F ϵ { R , C }, to the same class of matrices as the definition of Mitra and Puri.
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