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Sherman–Morrison formula : ウィキペディア英語版
Sherman–Morrison formula
In mathematics, in particular linear algebra, the Sherman–Morrison formula, named after Jack Sherman and Winifred J. Morrison, computes the inverse of the sum of an invertible matrix A
and the outer product, u v^T, of vectors u and 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.
== Statement ==
Suppose A is an invertible square matrix and u, v are column vectors. Suppose furthermore that 1 + v^T A^u \neq 0. Then the Sherman–Morrison formula states that
:(A+uv^T)^ = A^ - \over 1 + v^T A^u}.
Here, uv^T is the outer product of two vectors u and v. The general form shown here is the one published by Bartlett.

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