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Zbl 0967.15003
Hartwig, Robert E.; Wang, Guorong; Wei, Yimin
Some additive results on Drazin inverse. (English)
[J] Linear Algebra Appl. 322, No.1-3, 207-217 (2001). ISSN 0024-3795

Drazin inverses $(P+Q)^D$ of the sums of two matrices $P$ and $Q$ are considered [cf. {\it M. P. Drazin}, Am. Math. Mon. 65, 506-514 (1958; Zbl 0083.02901)]. The relation $(P+Q)^D =P^D+ Q^D$ provided $QP=PQ=0$ is extended to the case where only the one-sided condition $PQ=0$ is assumed. A formula for such noncommutative case is derived. Another extension is suggested for the case where only $P^2Q=0$ is assumed.
[Václav Burjan (Praha)]

MSC 2000:: *15A09 Matrix inversion
15A23 Factorization of matrices

Keywords: Drazin inverses; additive perturbations

Citations: Zbl 0083.02901

Cited in: Zbl 1157.47001 Zbl 1164.15307 Zbl 1071.15003 Zbl 1020.47001

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