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Note on the Generalized Invertibility of a-xy*
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  • Journal title : Kyungpook mathematical journal
  • Volume 55, Issue 2,  2015, pp.251-258
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2015.55.2.251
 Title & Authors
Note on the Generalized Invertibility of a-xy*
DU, FAPENG; XUE, YIFENG;
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 Abstract
Let be a unital -algebra, a, x and y are elements in . In this paper, we present the expression of the Moore-Penrose inverse and the group inverse of a- under the conditions , respectively.
 Keywords
Generalized inverse;Moore-Penrose inverse;Group inverse;
 Language
English
 Cited by
 References
1.
G. Chen, Y. Xue, The expression of generalized inverse of the perturbed operators under type I perturbation in Hilbert spaces, Linear Algebra Appl., 285(1998), 1-6. crossref(new window)

2.
Y. Chen, X. Hu, Q. Xu, The Moore-Penrose inverse of A - $XY^*$, J. Shanghai Normal Univer., 38(2009), 15-19.

3.
C. Deng, On the invertibility of the operator A - XB, Numb. Linear Algebra Appl., 16(2009), 817-831. crossref(new window)

4.
C. Deng, A generalization of the Sherman-Morrison-Woodbury formula, Appl. Math. Lett., 24(2011), 1561-1564. crossref(new window)

5.
C. Deng, On Moore-Penrose inverse of a kind of operators, Proceedings of the Ninth International Conference on Matrix Theory and Its Applications in China, (2010), 88-91.

6.
C. Deng, Y. Wei, Some New Results of the Sherman-Morrison-Woodbury Formula, Proceeding of The Sixth Iternational Conference of Matrices and Operators, 2(2011), 220-223.

7.
F. Du, Y. Xue, The expression of the Moore-Penrose inverse of A - $XY^*$, J. East China Normal Univ. (Nat. Sci.), 5(2010), 33-37.

8.
H. V. Hsnderson, Searl S. R., On deriving the inverse of a sum of matrices, Siam Review, 23(1)(1981), 53-60. crossref(new window)

9.
W. W. Hager, Updating the inverse of a matrix, Siam Review, 31(1989), 221-239. crossref(new window)

10.
Shani Jose, K. C. Sivakumar, Moore-Penrose Inverse of Perturbed Operators on Hilbert Spaces, Combinatorial Matrix Theory and Generalized Inverses of Matrices, (2013), 119-131.

11.
S. Kurt, A. Riedel, A Shermen-Morrison-Woodbury identity for rank augmenting matrices with application to centering, Siam J. Math. Anal., 12(1)(1991), 80-95.

12.
T. Steerneman, F. P. Kleij, Properties of the matrix A - $XY^*$, Linear Algebra Appl., 410(2005), 70-86. crossref(new window)

13.
Y. Xue, Stable Perturbations of Operators and Related Topics, World Scientific, (2012).