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A note on the representation for the Drazin inverse of 2×2 block matrices. (English) Zbl 1148.15001

The author gives the representations of the Drazin inverse of 2×2 block matrices under conditions weaker than those used in the following papers on the subject:

1. D. S. Djordjević and P. S. Stanimirović [Czech. Math. J. 51, No. 3, 617–634 (2001; Zbl 1079.47501)];

2. R. Hartwig, X. Li and Y. Wei [SIAM J. Matrix Anal. Appl. 27, No. 3, 757–771 (2006; Zbl 1100.15003)].

MSC:
15A09Matrix inversion, generalized inverses
References:
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[10]Djordjević, D. S.; Stanimirović, P. S.: On the generalized Drazin inverse and generalized resolvent, Czechoslovak math. J. 51, No. 126, 617-634 (2001) · Zbl 1079.47501 · doi:10.1023/A:1013792207970
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[13]Hartwig, R.; Li, X.; Wei, Y.: Representations for the Drazin inverse of 2×2 block matrix, SIAM J. Matrix anal. Appl. 27, 757-771 (2006) · Zbl 1100.15003 · doi:10.1137/040606685
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[16]Wang, G.; Wei, Y.; Qiao, S.: Generalized inverses: theory and computations, (2003)
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[19]Wei, Y.; Li, X.; Bu, F.; Zhang, F.: Relative perturbation bounds for the eigenvalues of diagonalizable and singular matrices – application of perturbation theory for simple invariant subspaces, Linear algebra appl. 419, 765-771 (2006) · Zbl 1151.15306 · doi:10.1016/j.laa.2006.06.015