Sherman-Morrison formula

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This is a useful identity:

\left [ A + a b^T \right ]^{-1} = A^{-1} - \frac{A^{-1} a b^T A^{-1}}{1 + b^T A^{-1} a},

where LaTeX: A is a nonsingular LaTeX: n \times n matrix and LaTeX: a and LaTeX: b are n-vectors, provided the inverse (on the left) exists.

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