The Woodbury formula (A + U V^T)^(-1) = A^(-1) - [A^(-1) U(I + V^T A^(-1) U)^(-1) V^T A^(-1)] is a formula that allows a perturbed matrix to be computed for a change to a given matrix A, where I is an identity matrix. This formula expands the scope of application of the Sherman-Morrison formula. In particular, in the Woodbury formula, U and V can be any (dimensionally compatible) matrices rather than simple row or column vectors u and v for the Sherman-Morrison formula.

Sherman-Morrison formula