Abstract
We consider nnd matrices A and B of the same order satisfying A⩾ B (i.e., A− B is nnd). Given an nnd ( i, j,…, p)-inverse A ( i, j,…, p) of A (or B ( i, j,… p) of B), we characterize nnd ( i, j,…, p)-inverses B ( i, j,…, p) of B (or A ( i, j,…, p) of A) such that the reverse ordering property B ( i, j,…, p) ⩾ A ( i, j,…, p) holds. We obtain a new characterization of (2)-inverses of a matrix and also characterize nnd generalized inverses of an nnd matrix which dominate or are dominated by a given nnd generalized inverse of the matrix.
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