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

Xiaoji Liu, Hongwei Jin and Jelena Višnjić

Mathematical Problems in Engineering, 2016, vol. 2016, 1-14

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.

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:9236281

DOI: 10.1155/2016/9236281

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