SingularValueList
gives a list of the nonzero singular values of a 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.
SingularValueList[{m,a},k]
gives the k largest generalized singular values of m.
Details and Options

- Singular values are sorted from largest to smallest.
- Repeated singular values appear with their appropriate multiplicity.
- SingularValueList[m,UpTo[k]] gives k singular values, or as many as are available.
- By default, singular values are kept only when they are larger than 100 times 10-p, where p 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]].
- Exact and symbolic matrices can be used, with zero tolerance assumed by default.
- The singular values can be obtained from Sqrt[Eigenvalues[ConjugateTranspose[m].m]].
Examples
open allclose allSee Also
SingularValueDecomposition Norm PseudoInverse Eigenvalues QRDecomposition SchurDecomposition NullSpace
Tutorials
Related Guides
Introduced in 2003
(5.0)
| Updated in 2015 (10.3)