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Mathematical Problems in Engineering
Volume 2016 (2016), Article ID 9236281, 14 pages
http://dx.doi.org/10.1155/2016/9236281
Research Article

Representations of Generalized Inverses and Drazin Inverse of Partitioned Matrix with Banachiewicz-Schur Forms

1Faculty of Science, Guangxi University for Nationalities, Nanning 530006, China
2Faculty of Medicine, University of Niš, 18000 Niš, Serbia

Received 15 July 2016; Accepted 6 September 2016

Academic Editor: Gen Qi Xu

Copyright © 2016 Xiaoji Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Representations of -inverses, -inverses, and Drazin inverse of a partitioned matrix related to the generalized Schur complement are studied. First, we give the necessary and sufficient conditions under which -inverses, -inverses, and group inverse of a block matrix can be represented in the Banachiewicz-Schur forms. Some results from the paper of Cvetković-Ilić, 2009, are generalized. Also, we expressed the quotient property and the first Sylvester identity in terms of the generalized Schur complement.