Svd - Maple Programming Help

Svd

compute the singular values/vectors of a numeric matrix

 Calling Sequence Svd(X) Svd(X, U,left) Svd(X, V,right) Svd(X, U, V)

Parameters

 X - n x p matrix U - (optional) the left singular vectors are to be returned in U V - (optional) the right singular vectors are to be returned in V

Description

 • Important:  The command Svd has been deprecated.  Use the  superseding command LinearAlgebra[SingularValues] instead.
 • Svd(X) returns a 1 by $\mathrm{min}\left(n,p\right)$ 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.

Examples

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

 > $A≔\mathrm{linalg}[\mathrm{matrix}]\left(2,2,\left[1,2,3,4\right]\right)$
 ${A}{:=}\left[\begin{array}{rr}{1}& {2}\\ {3}& {4}\end{array}\right]$ (1)
 > $\mathrm{evalf}\left(\mathrm{Svd}\left(A\right)\right)$
 $\left[\begin{array}{cc}{5.46498570421904}& {0.365966190626257}\end{array}\right]$ (2)