SingularValues[m]
gives the singular value decomposition for a numerical matrix . The result is a list
, where
is the list of singular values, and
can be written as ConjugateTranspose[u]. DiagonalMatrix[w].v.


SingularValues
SingularValues[m]
gives the singular value decomposition for a numerical matrix . The result is a list
, where
is the list of singular values, and
can be written as ConjugateTranspose[u]. DiagonalMatrix[w].v.
Details and Options

- SingularValues[m,Tolerance->t] specifies that singular values smaller than t times the maximum singular value are to be removed.
- The default setting Tolerance->Automatic typically takes
to be
where
is the numerical precision of the input.
- With Tolerance->0 singular values which are exactly zero can be returned.
and
are row orthonormal matrices, which can be considered as lists of orthonormal vectors.
- The ratio of the largest to smallest singular value gives the
condition number of
.
History
Introduced in 1988 (1.0)
Text
Wolfram Research (1988), SingularValues, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValues.html.
CMS
Wolfram Language. 1988. "SingularValues." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SingularValues.html.
APA
Wolfram Language. (1988). SingularValues. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SingularValues.html
BibTeX
@misc{reference.wolfram_2025_singularvalues, author="Wolfram Research", title="{SingularValues}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/SingularValues.html}", note=[Accessed: 08-August-2025]}
BibLaTeX
@online{reference.wolfram_2025_singularvalues, organization={Wolfram Research}, title={SingularValues}, year={1988}, url={https://reference.wolfram.com/language/ref/SingularValues.html}, note=[Accessed: 08-August-2025]}