Some Results on the Drazin Inverse of a Modified Matrix with New Conditions

Main Article Content

Abdul Shakoor, Hu Yang, Ilyas Ali

Abstract

In this article, we consider representations of the Drazin inverse of a modified matrix M = A-CDdB with the generalized Schur complement Z = D - BAdC under different conditions given in recent articles on the subject. Numerical example is given to illustrate our result.

Article Details

References

  1. A. Ben-Israel, T.N.E. Greville, Generalized Inverses: Theory and Applications, second ed., Springer, New York, 2003.
  2. S.L. Campbell, C.D. Meyer, Generalized Inverse of Linear Transformations, Dover, New York, 1991.
  3. G. Wang, Y. Wei, S. Qiao, Generalized Inverses: Theory and Computations, Science Press, Beijing/New York, 2004.
  4. J.M. Shoaf, The Drazin inverse of a rank-one modification of a square matrix, Ph.D. Dissertation, North Carolina State University, 1975.
  5. R. Kala, K. Klaczy ´nski, Generalized inverses of a sum of matrices, Sankhya Ser. A 56 (1994) 458-464.
  6. Y. Wei, The Drazin inverse of a modified matrix, Appl. Math. Comput. 125 (2002) 295-301.
  7. E. Dopazo, M.F. Mart ´inez-Serrano, On deriving the Drazin inverse of a modified matrix, Linear Algebra Appl. 438 (2013) 1678-1687.
  8. D. Mosi ´c, Some results on the Drazin inverse of a modified matrix, Calcolo. 50 (2013) 305?11.
  9. A. Shakoor, H. Yang, I. Ali, Some representations for the Drazin inverse of a modified matrix, Calcolo. DOI 10.1007/s10092-013-0098-0 (2013).