As is well known, the generalized inverse, Moore–Penrose inverse and group inverse are not continuous, i.e. for $\theta =\{1,2\},\{1,2,3,4\}$ and $\{1,2,5\}$, a linear bounded operator T has a θ-inverse $T^{\theta }$, the perturbed operator $\overline{T}=T+\delta T$ is not necessary θ-invertible and even if it is θ-invertible, $\underset{\delta T\to 0}{lim}{\overline{T}}^{\theta }=T^{\theta }$ may not be true. In this paper, we prove that $T+T{T}^{\theta }\delta T{T}^{\theta }T$ is θ-invertible and its θ-inverse $(T+T{T}^{\theta }\delta T{T}^{\theta }T{)}^{\theta }$ has the simplest possible expression, which satisfies $\underset{\delta T\to 0}{lim}(T+T{T}^{\theta }\delta T{T}^{\theta }T{)}^{\theta }=T^{\theta }$. Thus, we have found a continuous orbit for the generalized inverse, Moore–Penrose inverse and group inverse.

众所周知，广义逆，摩尔-彭罗斯逆和群逆不是连续的，即对于 $\theta =\{\mathrm{1个}，2\}，\{\mathrm{1个}，2，3，4\}$ 和 $\{\mathrm{1个}，2，5\}$，线性有界算子T具有θ逆${Ť}^{\theta }$，受干扰的运算符 $\overline{Ť}=Ť+\delta Ť$不必是θ可逆的，即使它是θ可逆的，$\underset{\delta Ť\to 0}{林}{\overline{Ť}}^{\theta }={Ť}^{\theta }$可能不是真的。在本文中，我们证明$Ť+Ť{Ť}^{\theta }\delta Ť{Ť}^{\theta }Ť$是θ-可逆且θ-逆$（Ť+Ť{Ť}^{\theta }\delta Ť{Ť}^{\theta }Ť{）}^{\theta }$ 具有最简单的表达式，可以满足 $\underset{\delta Ť\to 0}{林}（Ť+Ť{Ť}^{\theta }\delta Ť{Ť}^{\theta }Ť{）}^{\theta }={Ť}^{\theta }$。因此，我们发现了广义逆，摩尔-彭罗斯逆和群逆的连续轨道。