Journal of East China Normal University(Natural Sc

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Expressions on generalized inverses of the Schur complement of a 2×2 block matrix

GUO Mei-hua, LIU Ding-you   

  1. School of Mathematics and Statistics, Wuhan UniversityWuhan 430000, China
  • Received:2015-06-04 Online:2016-07-25 Published:2016-09-29

Abstract:

This article investigates various expressions for the generalized inverses of the Schur complement S = A − BD−C of a 2 × 2 block matrix M =
A B
C D
!
under different conditions. Moreover, we give some new results for the generalized inverses of the Schur complement when M is positive semidefinite. Besides, some conclusions are obtained directly from our results.

Key words: 2 ×, 2 block matrix, generalized inverse, Schur complement