A specific form of the general Sherman-Morrison formula reads
$(1+u v^T)^{-1}$ = $1 - \frac{u v^T}{1+v^T u}$
where $1$ is the identity matrix, $u,v$ are vectors (say with length n) and T denotes the transpose.
Is there a generalization of the formula to sums of outer products, i.e. for $(1+\sum\limits_{i=1}^{n} u_i v_i^T )^{-1} $ ?