Woodbury matrix identity (original) (raw)
In matematica, particolarmente in algebra lineare, l'identità matriciale di Woodbury o matrix inversion lemma per matrici di aspetto n × n è data dalla seguente formula: In essa A e UCV sono matrici di aspetto n × n, mentre C è una matrice quadrata che può avere aspetto diverso r × r; conseguentemente U ha aspetto n × r e V aspetto r × n.
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| dbo:abstract | Die Woodbury-Matrix-Identität, benannt nach Max A. Woodbury, besagt, dass die Inverse einer Rang--Korrektur einer Matrix als eine Rang--Korrektur der Inversen ausgedrückt werden kann. Gängig sind auch die Bezeichnungen Sherman-Morrison-Woodbury-Formel oder nur Woodbury-Formel. Doch die Gleichung wurde schon vor Woodburys Bericht erwähnt. Die Woodbury-Gleichung lautet , wobei , , und Matrizen des korrekten Formats bezeichnen. Genauer ist eine -Matrix, eine -Matrix, eine -Matrix und eine -Matrix. Im Spezialfall und , wird die Gleichung auch Sherman-Morrison-Formel genannt. Wenn die Einheitsmatrix ist, wird die Matrix oft genannt. (de) In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report. The Woodbury matrix identity is where A, U, C and V are conformable matrices: A is n×n, C is k×k, U is n×k, and V is k×n. This can be derived using blockwise matrix inversion. While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category. (en) In matematica, particolarmente in algebra lineare, l'identità matriciale di Woodbury o matrix inversion lemma per matrici di aspetto n × n è data dalla seguente formula: In essa A e UCV sono matrici di aspetto n × n, mentre C è una matrice quadrata che può avere aspetto diverso r × r; conseguentemente U ha aspetto n × r e V aspetto r × n. (it) Матрична тотожність Вудбері де матриці A розміру n×n, U розміру n×k, C розміру k×k і V розміру k×n. Використовується для обернення блочної матриці. (uk) |
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| dbp:title | Woodbury formula (en) |
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| rdfs:comment | In matematica, particolarmente in algebra lineare, l'identità matriciale di Woodbury o matrix inversion lemma per matrici di aspetto n × n è data dalla seguente formula: In essa A e UCV sono matrici di aspetto n × n, mentre C è una matrice quadrata che può avere aspetto diverso r × r; conseguentemente U ha aspetto n × r e V aspetto r × n. (it) Матрична тотожність Вудбері де матриці A розміру n×n, U розміру n×k, C розміру k×k і V розміру k×n. Використовується для обернення блочної матриці. (uk) Die Woodbury-Matrix-Identität, benannt nach Max A. Woodbury, besagt, dass die Inverse einer Rang--Korrektur einer Matrix als eine Rang--Korrektur der Inversen ausgedrückt werden kann. Gängig sind auch die Bezeichnungen Sherman-Morrison-Woodbury-Formel oder nur Woodbury-Formel. Doch die Gleichung wurde schon vor Woodburys Bericht erwähnt. Die Woodbury-Gleichung lautet , wobei , , und Matrizen des korrekten Formats bezeichnen. Genauer ist eine -Matrix, eine -Matrix, eine -Matrix und eine -Matrix. (de) In mathematics (specifically linear algebra), the Woodbury matrix identity, named after Max A. Woodbury, says that the inverse of a rank-k correction of some matrix can be computed by doing a rank-k correction to the inverse of the original matrix. Alternative names for this formula are the matrix inversion lemma, Sherman–Morrison–Woodbury formula or just Woodbury formula. However, the identity appeared in several papers before the Woodbury report. The Woodbury matrix identity is While the identity is primarily used on matrices, it holds in a general ring or in an Ab-category. (en) |
| rdfs:label | Woodbury-Matrix-Identität (de) Identità di Woodbury (it) Woodbury matrix identity (en) Матрична тотожність Вудбурі (uk) |
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