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As is well known, the generalized inverse, Moore–Penrose inverse and group inverse are not continuous, i.e. for  θ  = {1, 2}, {1, 2, 3, 4} and {1, 2, 5}, a linear bounded operator  T  has a  θ -inverse, the perturbed operatoris not necessary  θ -invertible and even if it is  θ -invertible,may not be true. In this paper, we prove thatis  θ -invertible and its  θ -inversehas the simplest possible expression, which satisfies. Thus, we have found a continuous orbit for the generalized inverse, Moore–Penrose inverse and group inverse.

A continuous orbit for the generalized inverse, Moore–Penrose inverse and group inverse