SingularValues

Since Version 5.0 (released in 2003), SingularValues has been superseded by SingularValueList and SingularValueDecomposition.

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 .
Wolfram Research (1988), SingularValues, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValues.html.

Text

Wolfram Research (1988), SingularValues, Wolfram Language function, https://reference.wolfram.com/language/ref/SingularValues.html.

BibTeX

@misc{reference.wolfram_2021_singularvalues, author="Wolfram Research", title="{SingularValues}", year="1988", howpublished="\url{https://reference.wolfram.com/language/ref/SingularValues.html}", note=[Accessed: 25-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_singularvalues, organization={Wolfram Research}, title={SingularValues}, year={1988}, url={https://reference.wolfram.com/language/ref/SingularValues.html}, note=[Accessed: 25-September-2021 ]}

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