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.
- 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 allScope (4)
Generalizations & Extensions (2)
Options (2)
Tolerance (2)
Compute the singular values larger than of the largest singular value:
Setting Tolerance to will directly compute the same set of singular values:
The matrix is positive definite, so with exact arithmetic there are 16 nonzero singular values:
Many of the singular values are too small to show up at machine precision:
Setting the tolerance to zero will make them all show up:
Because of numerical roundoff, the values are not computed accurately:
Applications (1)
Properties & Relations (1)
m is a matrix of random size having random entries:
Find the singular values of m:
These are equal to the square roots of the nonzero eigenvalues of m.Transpose[m]:
Text
Wolfram Research (2003), SingularValueList, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValueList.html (updated 2015).
BibTeX
BibLaTeX
CMS
Wolfram Language. 2003. "SingularValueList." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2015. https://reference.wolfram.com/language/ref/SingularValueList.html.
APA
Wolfram Language. (2003). SingularValueList. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SingularValueList.html