Say I have a matrix $M$ and know its inverse $M^{-1}$. Then every element changes so that $M'=M+(M'-M)$. Is there a fast way to find $M'^{-1}$ from this information? That is without computing the new inverse from scratch (naively a $\mathcal{O}(n^3)$ calculation)?
2026-03-31 03:32:05.1774927925
Compute new inverse when old inverse and new and old matrix known
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