About: Sherman–Morrison formula

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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 and the outer product, , of vectors and . The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after Sherman and Morrison, it appeared already in earlier publications.

Attributes	Values
rdfs:label	Sherman-Morrison-Woodbury-Formel (de) Wzór Shermana-Morrisona (pl) Sherman–Morrison formula (en)
rdfs:comment	Die Sherman-Morrison-Woodbury-Formel (nach Jack Sherman, Winifred J. Morrison und Max A. Woodbury) der linearen Algebra gibt eine explizite Darstellung der Inversen einer regulären Matrix nach einer Änderung von niederem Rang. Dies ist beispielsweise bei Quasi-Newton-Verfahren und beim Basiswechsel im Simplex-Verfahren interessant. In numerischen Verfahren kann die Verwendung der Formel zu Stabilitätsproblemen führen, weswegen Alternativen zu bevorzugen sind. (de) 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 and the outer product, , of vectors and . The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after Sherman and Morrison, it appeared already in earlier publications. (en) Wzór Shermana-Morrisona – wzór służący do obliczenia odwrotności sumy macierzy odwracalnej i iloczynu diadycznego wektorów i Wzór Shermana-Morrisona jest szczególnym przypadkiem wzoru Shermana-Morrisona-Woodbury’ego. Nazwany na cześć Shermana i Morrisona, pojawiał się jednak we wcześniejszych publikacjach. (pl)
dcterms:subject	Matrix theory Linear algebra
Wikipage page ID	2556798 (xsd:integer)
Wikipage revision ID	1117542371 (xsd:integer)
Link from a Wikipage to another Wikipage	Determinant Column vector Mathematics Matrix (mathematics) Quasi-Newton method Linear algebra Computational complexity theory Identity matrix Perturbation theory Maxwell stress tensor Matrix determinant lemma Matrix theory Square matrix Linear algebra Binomial inverse theorem Rank (linear algebra) Invertible Woodbury matrix identity Bunch–Nielsen–Sorensen formula If and only if Outer product Inverse matrix Vector (mathematics) Computationally expensive
sameAs	Sherman–Morrison formula Sherman–Morrison formula Sherman–Morrison formula Sherman–Morrison formula Sherman–Morrison formula Sherman–Morrison formula
dbp:wikiPageUsesTemplate	dbt:Circular_reference dbt:MathWorld dbt:Reflist dbt:Short_description dbt:Use_American_English
title	Sherman–Morrison formula (en)
urlname	Sherman-MorrisonFormula (en)
has abstract	Die Sherman-Morrison-Woodbury-Formel (nach Jack Sherman, Winifred J. Morrison und Max A. Woodbury) der linearen Algebra gibt eine explizite Darstellung der Inversen einer regulären Matrix nach einer Änderung von niederem Rang. Dies ist beispielsweise bei Quasi-Newton-Verfahren und beim Basiswechsel im Simplex-Verfahren interessant. In numerischen Verfahren kann die Verwendung der Formel zu Stabilitätsproblemen führen, weswegen Alternativen zu bevorzugen sind. (de) 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 and the outer product, , of vectors and . The Sherman–Morrison formula is a special case of the Woodbury formula. Though named after Sherman and Morrison, it appeared already in earlier publications. (en) Wzór Shermana-Morrisona – wzór służący do obliczenia odwrotności sumy macierzy odwracalnej i iloczynu diadycznego wektorów i Wzór Shermana-Morrisona jest szczególnym przypadkiem wzoru Shermana-Morrisona-Woodbury’ego. Nazwany na cześć Shermana i Morrisona, pojawiał się jednak we wcześniejszych publikacjach. (pl)
prov:wasDerivedFrom	wikipedia-en:Sherman–Morrison_formula?oldid=1117542371&ns=0
page length (characters) of wiki page	9376 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Sherman–Morrison_formula
is Link from a Wikipage to another Wikipage of	List of mathematical identities Jack Sherman (statistician) Matroid parity problem Quasi-Newton method Cross-validation (statistics) Maxwell stress tensor Matrix determinant lemma Broyden's method Woodbury matrix identity Bunch–Nielsen–Sorensen formula Broyden–Fletcher–Goldfarb–Shanno algorithm Tridiagonal matrix algorithm Sherman-Morrison formula Sherman-Morrison Formula Sherman-morrison Winifred J. Morrison
is Wikipage redirect of	Jack Sherman (statistician) Sherman-Morrison formula Sherman-Morrison Formula Sherman-morrison Winifred J. Morrison
is foaf:primaryTopic of	wikipedia-en:Sherman–Morrison_formula

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