SingularValueList

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

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

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

Singular values are sorted from largest to smallest.

Repeated singular values appear with their appropriate multiplicity.

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

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

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

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

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

See Section 3.7.10.

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

Related packages: Statistics`LinearRegression`.

New in Version 5.0.

Further Examples