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

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  • Xiaoji Liu
  • Hongwei Jin
  • Jelena Višnjić

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.

Suggested Citation

  • Xiaoji Liu & Hongwei Jin & Jelena Višnjić, 2016. "Representations of Generalized Inverses and Drazin Inverse of Partitioned Matrix with Banachiewicz-Schur Forms," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-14, October.
  • Handle: RePEc:hin:jnlmpe:9236281
    DOI: 10.1155/2016/9236281
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