On group inverses and the sharp order

Mitra, Sujit Kumar (1987) On group inverses and the sharp order Linear Algebra and its Applications, 92 . pp. 17-37. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002437...

Related URL: http://dx.doi.org/10.1016/0024-3795(87)90248-5


In this work the group inverse of a matrix is used to define the #-order on square matrices of index 1. The #-order is similar to the *-order of Drazin [2] and the minus order of Hartwig [6, 10] and Nambooripad [17]. The #-order and the *-order are compared and contrasted. Many conditions are given which assure the equivalence of the various partial orders studied.

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