A note of the representation of the Drazin inverse of 2x2 block matrix

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References[1] A. Ben-Israel and T. N. E. Greville, Generalized Inverses: Theory andApplications, 2nd Edition, Springer Verlag, New York, 2003.[2] S. L. Campbell, Singular Systems of Differential Equations, Pitman,London, 1980.[3] S. L. Campbell, The Drazin inverse and systems of second order lineardifferential equations, Linear and Multilinear Algebra, 14 (1983) 195-198.[4] S. L. Campbell and C. D. Meyer, Generalized Inverse of Linear Transformations,Pitman, London, 1979, Dover, New York, 1991.[5] N. Castro-González, E. Dopazo and J. Robles, Formulas for the Drazininverse of special block matrices, Appl. Math. Comput., 174 (2006) 252-270.[6] N. Castro González, J.J. Koliha, New additive results for the g-Drazininverse, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 1085-1097.[7] X. Chen, R.E. Hartwig, The group inverse of a triangular matrix, LinearAlgebra Appl., 237/238 (1996) 97-108.[8] D. S. Cvetković-Ilić, D. S. Djordjević and Y. Wei, Additive results forthe generalized Drazin inverse in a Banach algebra, Linear Algebra andIts Appl., 418 (2006), 53-61.[9] D. S. Djordjević and P. S. Stanimirović, On the generalized Drazin inverseand generalized resolvent, Czechoslovak Math. J., 51(126) (2001)617-634.[10] M.P. Drazin, Pseudoinverse in associative rings and semigroups, Amer.Math. Monthly 65 (1958) 506–514.[11] R. E. Hartwig and J. M. Shoaf, Group inverses and Drazin inverses ofbidiagonal and triangular Toeplitz matrices, Austral. J. Math., 24(A)(1977) 10-34.[12] R. Hartwig, X. Li and Y. Wei, Representations for the Drazin inverseof 2 × 2 block matrix, SIAM J. Matrix Anal. Appl., 27 (2006) 757-771.[13] R. E. Hartwig, G. Wang and Y. Wei, Some additive results on Drazininverse, Linear Algebra Appl., 322 (2001) 207-217.8
[14] C.D. Meyer and N.J. Rose, The index and the Drazin inverse of blocktriangular matrices, SIAM J. Appl. Math., 33 (1977) 1-7.[15] X. Li and Y. Wei, An expression of the Drazin inverse of a perturbedmatrix, Appl. Math. Comput., 153 (2004) 187-198.[16] G. Wang, Y. Wei, S. Qiao, Generalized inverses: theory and computations,Science Press, 2003.[17] X. Li, Y. Wei, A note on the representations for the Drazininverse of 2 × 2 block matrices, Linear Algebra Appl., (2007),doi:10.1016/j.laa.2007.01.005.[18] Y. Wei, Expression for the Drazin inverse of a 2×2 block matrix, Linearand Multilinear Algebra, 45 (1998) 131-146.[19] Y. Wei, X. Li, F. Bu, F. Zhang, Relative perturbation bounds for theeigenvalues of diagonalizable and singular matrices-application of perturbationtheory for simple invariant subspaces, Linear Algebra Appl.,419 (2006) 765–771.Address:Dragana S. Cvetković-Ilić:Department of Mathematics, Faculty of Sciences, University of Niš, P.O.Box 224, Višegradska 33, 18000 Niš, SerbiaE-mail: dragana@pmf.ni.ac.yu gagamaka@ptt.yu9
Page 1: A note on the representation for th
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Page 6 and 7: [ A BTheorem 2.3 Let M =C Done of t

A note of the representation of the Drazin inverse of 2x2 block matrix

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