Sherman–Morrison formula
Formula computing the inverse of the sum of a matrix with the outer product of two vectors
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. That is, given an invertible matrix A {\displaystyle A} and the outer product u v T {\displaystyle uv^{\textsf {T}}} of vectors u {\displaystyle u} and v , {\displaystyle v,} the formula cheaply computes an updated matrix inverse ( A + u v T ) ) − 1 . {\textstyle \left(A+uv^{\textsf {T}}\right){\vphantom {)}}^{\!-1}.} The Sherman–Morrison formula is...
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Sherman–Morrison formula
Formula computing the inverse of the sum of a matrix with the outer product of two vectors
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. That is, given an invertible matrix A {\displaystyle A} and the outer product u v T {\displaystyle uv^{\textsf {T}}} of vectors u {\displaystyle u} and v , {\displaystyle v,} the formula cheaply computes an updated matrix inverse ( A + u v T ) ) − 1 . {\textstyle \left(A+uv^{\textsf {T}}\right){\vphantom {)}}^{\!-1}.} The Sherman–Morrison formula is...
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From Wikipedia
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. That is, given an invertible matrix A {\displaystyle A} and the outer product u v T {\displaystyle uv^{\textsf {T}}} of vectors u {\displaystyle u} and v , {\displaystyle v,} the formula cheaply computes an updated matrix inverse ( A + u v T ) ) − 1 . {\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.
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