I've read a paper in which the authors said that they use the "Sherman-Morrison inverse formula". While I know the Sherman-Morrison formula, I couldn't find anything about the inverse of said formula. Based on the equations in the paper the formula should look something like this: $$ A^{-1} + uv^T = A - \frac{Auv^TA}{1 + v^TAu}$$
Does this formula exist? Can anyone point me in the right direction in terms of literature?