BUILT-IN MATHEMATICA SYMBOL

# 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 OptionsDetails 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 , 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]].

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

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

 Out[1]=