gives a list of the nonzero singular values of a matrix m.


gives the generalized singular values of m with respect to a.


gives the k largest singular values of m.


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[Conjugate[Transpose[m]].m]].


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Basic Examples  (1)

There are only two nonzero singular values since the matrix is singular:

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Scope  (4)

Generalizations & Extensions  (2)

Options  (2)

Applications  (1)

Properties & Relations  (1)

Possible Issues  (1)

See Also

SingularValueDecomposition  Norm  PseudoInverse  Eigenvalues  QRDecomposition  SchurDecomposition  NullSpace


Introduced in 2003
| Updated in 2015