SingularValueDecomposition

SingularValueDecomposition[m] gives the singular value decomposition for a numerical matrix m. The result is 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.

The matrix m may be rectangular.

The diagonal elements of w are the singular values of m.

SingularValueDecomposition sets to zero any singular values that would be dropped by SingularValueList.

The option Tolerance can be used as in SingularValueList to determine which singular values will be considered to be zero.

u and v are column orthonormal matrices, whose transposes can be considered as lists of orthonormal vectors.

SingularValueDecomposition[m, a] gives a list of matrices u, ua, w, wa, v such that m can be written as u . w . Conjugate[Transpose[v]] and a can be written as ua . wa . Conjugate[Transpose[v]].

See Section 3.7.10.

Implementation Notes: see Section A.9.4.

See also: SingularValueList, Norm, PseudoInverse, QRDecomposition.

Related packages: Statistics`LinearRegression`.

New in Version 5.0.

Further Examples