the Woodbury matrix identity, named after Max A. Woodbury[1][2] 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–...
4、l partial differential equationsas the capacitance matrix.3direct proof just check that times the rhs of the woodbury identity gives the identity matrix: derivation via blockwise elimination deriving the woodbury matrix identity is easily done by solving the following block matrix inversion problem ...
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 ...
the Woodbury matrix identity, named after Max A. Woodbury[1][2] 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–Morri...
The Sherman–Morrison–Woodbury formula is straightforward to verify, by showing that the product of the two sides is the identity matrix. How can the formula be derived in the first place? Consider any two matrices and such that and
IisanidentitymatrixandboththematricesAandI+V∗A−1Uarenonsingular.Inmathematics(specificallylinearalgebra),thismatrixidentitysaysthattheinverseofalowerrankcorrectionofsomematrixcanbecomputedbydoingalowerrankcorrectiontotheinverseoftheoriginalmatrix.Alternativenamesforthisformulaarethematrixinversionlemma,Sherman-...
In mathematics (specifically linear algebra), this matrix identitysays that the inverse of a lower rank correction of some matrix can be computedby doing a lower rank correction to the inverse of the original matrix. Alternativenames for this formula are the matrix inversion lemma, Sherman-...
the Woodbury matrix identity, named after Max A. Woodbury[1][2] 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–Morri...