SingularValueDecomposition

SingularValueDecomposition[m]

gives the singular value decomposition for a numerical matrix m as a list of matrices {u,w,v}, where w is a diagonal matrix and m can be written as u.w.Conjugate[Transpose[v]].

SingularValueDecomposition[{m,a}]

gives the generalized singular value decomposition of m with respect to a.

SingularValueDecomposition[m,k]

gives the singular value decomposition associated with the k largest singular values of m.

SingularValueDecomposition[m,UpTo[k]]

gives the decomposition for the k largest singular values, or as many as are available.

SingularValueDecomposition[{m,a},k]

gives the generalized singular value decomposition associated with the k largest singular values.

Details and Options

Examples

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Basic Examples  (1)

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Scope  (3)

Generalizations & Extensions  (3)

Options  (1)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (1)

See Also

SingularValueList  Norm  PseudoInverse  LeastSquares  QRDecomposition  SchurDecomposition

Tutorials

Introduced in 2003
(5.0)
| Updated in 2015
(10.3)