For
$ρ(B_gB- A^DA) < 1,$
where
The acute perturbation coincides with the stable perturbation of the group inverse, if the matrix
${\mathcal R}(B) \cap {\mathcal N}(A^k) = \{ {\bf 0} \}, {\mathcal N}(B)\cap {\mathcal R}(A^k) = \{ {\bf 0} \}$
which introduced by Vélez-Cerrada, Robles, and Castro-González, (Error bounds for the perturbation of the Drazin inverse under some geometrical conditions, Appl. Math. Comput., 215 (2009), 2154-2161).
Furthermore, two examples are provided to illustrate the acute perturbation of the Drazin inverse. We prove the correctness of the conjecture in a special case of ind
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