Journal of East China Normal University(Natural Sc ›› 2010, Vol. 2010 ›› Issue (5): 33-37,4.

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Expression of the Moore-Penrose inverse of A-XY*

DU Fa-peng1,2, XUE Yi-feng1   

  1. 1. Department of Mathematics, East China Normal University, Shanghai 200241, China; 2. College of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou Jiangsu 221008, China
  • Received:2010-01-01 Revised:2010-05-01 Online:2010-09-25 Published:2010-09-25
  • Contact: DU Fa-peng

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Abstract: By using theory of bounded linear operators on Hilbert spaces, the Shermen-Morrison-Woodbury (SMW) formula's Moore-Penrose inverse was presented. The formula obtained can be used to compute certain perturbation of A^+ and the Moore--Penrose inverses of some operator matrices.

Key words: Moore-Penrose inverse, idempotent operator, Hilbert space, Moore-Penrose inverse, idempotent operator

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