# 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 all

## Basic Examples(1)

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

 In[1]:=
 Out[1]=