# 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

#### Dear Wikiwand AI, let's keep it short by simply answering these key questions:

Can you list the top facts and stats about Winifred J. Morrison?

Summarize this article for a 10 year old

SHOW ALL QUESTIONS

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]}