# Sherman–Morrison formula

## Formula computing the inverse of the sum of a matrix and the outer product of two vectors / From Wikipedia, the free encyclopedia

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In linear algebra, the **Sherman–Morrison formula**, named after Jack Sherman and Winifred J. Morrison, computes the inverse of a "rank-1 update" to a matrix whose inverse has previously been computed.^{[1]}^{[2]}^{[3]} That is, given an invertible matrix $A$ and the outer product $uv^{\textsf {T}}$ of vectors $u$ and $v,$ the formula cheaply computes an updated matrix inverse ${\textstyle \left(A+uv^{\textsf {T}}\right){\vphantom {)}}^{\!-1}.}$

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]}