I recently came across this tweet about the Sherman-Morrison-Woodbury formula (henceforth referred to as SMW in this post). I was reading linear regression and I realized that this formula has a very practical application there. I will highlight the formula and briefly explain one of its applications. The Sherman-Morrison-Woodbury formula is : $$(A + uv^T)^{-1} = A^{-1} - \frac{A^{-1}uv^TA^{-1}}{1+v^TA^{-1}u}$$ where $A$ is n $\times$ n matrix and $u$ and $v$ are both n $\times$ 1 matrix. ... Read more