A seemingly simple question (but not a HW problem). Let $||\cdot||$ be the operator norm and $||\cdot||_F$ be the Frobenius norm. Say that $A, B\in R^{n\times n}$ are symmetric positive definite. Is it possible to find an upper bound for $||A^{-1}-B^{-1}||_F$ as a function of $||A-B||$ and, additionally, $||A||$ or $||A^{-1}||$?
2026-03-28 21:51:22.1774734682
Bounding the norm of the difference of matrix inverses
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