I'm curious about the following: if we know that for two matrices $A,B$ of full rank that $||A-B||_F < \epsilon$ for some $\epsilon$, is there a bound that can be given on $||(A^TA)^{-1} - (B^TB)^{-1}||_F$?
(Where $||\cdot||_F$ is the square root of sum of squares of entries of the matrix)
I don't know if this comes under matrix perturbation theory or not, but any thoughts or references would be helpful.