Continental Shelf, Linear Algebra
The Sherman-Morrison-Woodbury formula expresses the inverse of an “update” to a matrix $A$ in terms of $A^{-1}$ and the factors of the update: $$\displaystyle (A + UCV)^{-1} = A^{-1} – A^{-1} U\left( C^{-1} + VA^{-1}U \right)^{-1}VA^{-1} $$ where $A$ and $C$ are invertible square matrices and $U$ and $V$ have dimensions such that $UCV$ has … Read More “Sherman-Morrison-Woodbury for Determinants” »