This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

Documentation / Mathematica / Built-in Functions / Numerical Computation / Matrix Operations /

SingularValueDecomposition

FilledSmallSquare 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]].

FilledSmallSquare SingularValueDecomposition[m, a] gives the generalized singular value decomposition of m with respect to a.

FilledSmallSquare SingularValueDecomposition[m, k] gives the singular value decomposition associated with the k largest singular values of m.

FilledSmallSquare The matrix m may be rectangular.

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

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

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

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

FilledSmallSquare 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]].

FilledSmallSquare See Section 3.7.10.

FilledSmallSquare Implementation Notes: see Section A.9.4.

FilledSmallSquare See also: SingularValueList, Norm, PseudoInverse, QRDecomposition.

FilledSmallSquare Related packages: Statistics`LinearRegression`.

FilledSmallSquare New in Version 5.0.

Further Examples