Abstract and Applied Analysis

Extension of the GSMW Formula in Weaker Assumptions

Wenfeng Wang and Xi Chen

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this note, the generalized Sherman-Morrison-Woodbury (for short GSMW) formula ( A + Y G Z ) = A A Y ( G + Z A Y ) Z A is extended under some assumptions weaker than those used by Duan, 2013.

Article information

Abstr. Appl. Anal., Volume 2014 (2014), Article ID 324836, 2 pages.

First available in Project Euclid: 2 October 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Wang, Wenfeng; Chen, Xi. Extension of the GSMW Formula in Weaker Assumptions. Abstr. Appl. Anal. 2014 (2014), Article ID 324836, 2 pages. doi:10.1155/2014/324836. https://projecteuclid.org/euclid.aaa/1412276955

Export citation


  • M. S. Bartlett, “An inverse matrix adjustment arising in discriminant analysis,” Annals of Mathematical Statistics, vol. 22, pp. 107–111, 1951.
  • J. Sherman and W. J. Morrison, “Adjustment of an inverse matrix corresponding to a change in one element of a given matrix,” Annals of Mathematical Statistics, vol. 21, pp. 124–127, 1950.
  • M. A. Woodbury, “Inverting Modified Matrices,” Tech. Rep. 42, Statistical Research Group, Princeton University, Princeton, NJ, USA, 1950.
  • A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory and Applications, Springer, New York, NY, USA, 2nd edition, 2003.
  • W. W. Hager, “Updating the inverse of a matrix,” SIAM Review, vol. 31, no. 2, pp. 221–239, 1989.
  • C. Y. Deng, “A generalization of the Sherman-Morrison-Woodbury formula,” Applied Mathematics Letters, vol. 24, no. 9, pp. 1561–1564, 2011.
  • T. Steerneman and F. van Perlo-ten Kleij, “Properties of the matrix $A-X{Y}^{x}2a;$,” Linear Algebra and Its Applications, vol. 410, pp. 70–86, 2005.
  • Y.-N. Dou, G.-C. Du, C.-F. Shao, and H.-K. Du, “Closedness of ranges of upper-triangular operators,” Journal of Mathematical Analysis and Applications, vol. 356, no. 1, pp. 13–20, 2009.
  • Y. T. Duan, “A generalization of the SMW formula of operator $A+YG{Z}^{x}2a;$ to the $\{2\}$-inverse case,” Abstract and Applied Analysis, vol. 2013, Article ID 694940, 4 pages, 2013. \endinput