Important:  The command Svd has been deprecated.  Use the  superseding command LinearAlgebra[SingularValues] instead.

Svd(X) returns a 1 by $\min \left(n\,p\right)$ array of the singular values of X.

The entries of X must be all numerical.

Svd(X,U,`left`) returns the singular values and the left singular vectors in U.

Svd(X,V,`right`) returns the singular values and the right singular vectors in V.

Svd(X,U,V) returns the singular values and the left and right singular vectors in U and V respectively. The singular vectors together with the singular values satisfy $U\'\mathrm{XV}=\mathrm{D}$ where U' is the transpose of U and U is n by n, V is p by p, X is n by p, and D is n by p where ${\mathrm{D}}_{i,i}$ is/are the singular value/values of X.

This procedure Svd is compatible with the Fortran library linpack.

Note that nothing happens when the user invokes Svd(X) (same for other calling sequences); the user must use evalf(Svd(X)) to actually compute the singular values and singular vectors.

$A≔\mathrm{linalg}\left[\mathrm{matrix}\right]\left(2\,2\,\left[1\,2\,3\,4\right]\right)$

$A≔\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]$

$\mathrm{evalf}\left(\mathrm{Svd}\left(A\right)\right)$

$\left[\begin{array}{cc}5.46498570421904& 0.365966190626257\end{array}\right]$