Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X43720171230Perturbation bounds for $g$-inverses with respect to the unitarily invariant norm265526621256ENL.MengCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, P.R. China.Journal Article20170630Let complex matrices $A$ and $B$ have the same sizes. Using the singular value decomposition, we characterize the $g$-inverse $B^{(1)}$ of $B$ such that the distance between a given $g$-inverse of $A$ and the set of all $g$-inverses of the matrix $B$ reaches minimum under the unitarily invariant norm. With this result, we derive additive and multiplicative perturbation bounds of the nearest perturbed $g$-inverse. These results generalize and improve the existing results published recently to some extent.http://bims.iranjournals.ir/article_1256_48f9f6287f956af831c7368cb1ae09b4.pdf