151
Views
1
CrossRef citations to date
0
Altmetric
Section B

The perturbation of the Drazin inverse

, &
Pages 711-726 | Received 30 Sep 2011, Accepted 19 Dec 2011, Published online: 13 Feb 2012

References

  • Campbell , S. L. and Meyer , C. D. 1979 . Generalized Inverse of Linear Transformations , Boston , MA : Pitman (Advanced Publishing Program) . (reprinted by Dover, 1991)
  • Castro-González , N. and Koliha , J. J. 2000 . Perturbation of the Drazin inverse for closed linear operators . Integr. Equations Oper. Theory , 36 : 92 – 106 .
  • Castro-González , N. , Robles , J. and Vélez-Cerrada , J. Y. 2008 . Characterizations of a class of matrices and perturbation of the Drazin inverse . SIAM J. Matrix Anal. Appl , 30 ( 2 ) : 882 – 897 .
  • Deng , C. and Wei , Y. 2010 . Perturbation of the generalized Drazin inverse . Electron. J. Linear Algebra , 21 : 85 – 97 .
  • Hartwig , R. E. , Wang , G. and Wei , Y. 2001 . Some additive results on Drazin inverse . Linear Algebra Appl , 322 : 207 – 217 .
  • Herrero , A. , Ramírez , F. and Thome , N. Relationships between different sets involving group and Drazin projectors and nonnegativity . Linear Algebra Appl , in press, doi:10.1016/j.laa.2011.08.029
  • Horn , R. A. and Johnson , C. R. 1985 . Matrix Analysis , Cambridge , , UK : Cambridge University Press . (reprinted with corrections 1990)
  • Kirkland , S. 1995 . The group inverse associated with an irreducible periodic nonnegative matrix . SIAM J. Matrix Anal. Appl , 16 ( 4 ) : 1127 – 1134 .
  • Li , X. , Xu , L. and Yu , Y. The explicit expression of the Drazin inverse of sums of two matrices and its application . Italian J. Pure Appl. Math , (in press)
  • Meyer , C. D. and Rose , N. J. 1977 . The index and the Drazin inverse of block triangular matrices . SIAM J. Appl. Math , 33 : 1 – 7 .
  • Vélez-Cerrada , J. Y. , Robles , J. and Castro-González , N. 2009 . Error bounds for the perturbation of the Drazin inverse under some geometrical conditions . Appl. Math. Comput , 215 ( 6 ) : 2154 – 2161 .
  • Wang , G. , Wei , Y. and Qiao , S. 2004 . Generalized Inverses: Theory and Computations , Beijing : Science Press .
  • Wei , Y. 2000 . The Drazin inverse of updating of a square matrix with application to perturbation formular . Appl. Math. Comput , 108 : 77 – 83 .
  • Wei , Y. 2002 . Perturbation bound of the Drazin inverse . Appl. Math. Comput , 125 : 231 – 244 .
  • Wei , Y. and Deng , C. 2011 . A note on additive results for the Drazin inverse . Linear Multilinear Algebra , 59 ( 12 ) : 1319 – 1329 .
  • Wei , Y. and Wang , G. 1997 . The perturbation theory for the Drazin inverse and its applications . Linear Algebra Appl , 258 : 179 – 186 .
  • Xu , Q. , Song , C. and Wei , Y. 2009 . The stable perturbation of the Drazin inverse of the square matrices . SIAM J. Matrix Anal. Appl , 31 ( 3 ) : 1507 – 1520 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.