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 / Lists and Matrices / Matrix Operations /


FilledSmallSquare SingularValueList[m] gives a list of the non-zero singular values of a numerical matrix m.

FilledSmallSquare SingularValueList[m, a] gives the generalized singular values of m with respect to a.

FilledSmallSquare SingularValueList[m, k] gives the k largest singular values of m.

FilledSmallSquare Singular values are sorted from largest to smallest.

FilledSmallSquare Repeated singular values appear with their appropriate multiplicity.

FilledSmallSquare By default, singular values are kept only when they are larger than 100 times , where is Precision[m].

FilledSmallSquare SingularValueList[m, Tolerance->t] keeps only singular values that are at least t times the largest singular value.

FilledSmallSquare SingularValueList[m, Tolerance->0] returns all singular values.

FilledSmallSquare The matrix m can be rectangular; the total number of singular values is always Min[Dimensions[m]].

FilledSmallSquare The singular values can be obtained from Sqrt[Eigenvalues[Conjugate[Transpose[m]] . m]].

FilledSmallSquare See Section 3.7.10.

FilledSmallSquare See also: SingularValueDecomposition, Norm, PseudoInverse, Eigenvalues, QRDecomposition, SchurDecomposition.

FilledSmallSquare Related packages: Statistics`LinearRegression`.

FilledSmallSquare New in Version 5.0.

Further Examples