Woodbury Matrix Identity
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High Quality Content by WIKIPEDIA articles! 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. This identity is useful in certain numerical computations where A 1 has already been computed and it is…mehr

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High Quality Content by WIKIPEDIA articles! 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. This identity is useful in certain numerical computations where A 1 has already been computed and it is desired to compute (A + UCV) 1. With the inverse of A available, it is only necessary to find the inverse of C 1 + VA 1U in order to obtain the result using the right-hand side of the identity. If C has a much smaller dimension than A, this is more efficient than inverting A + UCV directly.