# Sherman–Morrison formula

In mathematics, in particular linear algebra, the Sherman–Morrison formula,[1][2][3] named after Jack Sherman and Winifred J. Morrison, computes the inverse of the sum of an invertible matrix ${\displaystyle A}$ and the outer product, ${\displaystyle uv^{\textsf {T}}}$, of vectors ${\displaystyle u}$ and ${\displaystyle v}$. The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after Sherman and Morrison, it appeared already in earlier publications.[4]