svd - Maple Help

MTM

 svd
 compute the singular values of a matrix

 Calling Sequence S = svd(A) [U,S,V] = svd(A)

Parameters

 A - matrix, vector, array, or scalar

Description

 • The function svd(A) computes the singular values and left and right singular vectors of matrix A.
 • When the function is called using the form S = svd(A), the returned value of S is a column vector containing the singular values of A.
 • When the function is called using the form U,S,V := svd(A), the returned value of U is a matrix whose columns are the left singular vectors of A. The returned value of S is a column vector containing the singular values of A.  The returned value of V is a matrix whose columns are the right singular vectors of A.

Examples

 > $\mathrm{with}\left(\mathrm{MTM}\right):$
 > $A≔\mathrm{Matrix}\left(\left[\left[1,2,1\right],\left[2,4,2\right],\left[2,8,1\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{1}& {2}& {1}\\ {2}& {4}& {2}\\ {2}& {8}& {1}\end{array}\right]$ (1)
 > $\mathrm{svd}\left(A\right)$
 $\left[\begin{array}{c}{0}\\ \frac{\sqrt{{198}{+}{2}{}\sqrt{{8741}}}}{{2}}\\ \frac{\sqrt{{198}{-}{2}{}\sqrt{{8741}}}}{{2}}\end{array}\right]$ (2)
 > $U,S,V≔\mathrm{svd}\left(A\right)$
 ${U}{,}{S}{,}{V}{≔}\left[\begin{array}{ccc}{-0.241424496932006}& {-0.376449481711859}& {-0.894427190999916}\\ {-0.482848993864012}& {-0.752898963423719}& {0.447213595499958}\\ {-0.841766631202282}& {0.539841586573656}& {0.}\end{array}\right]{,}\left[\begin{array}{ccc}{9.81053809097800}& {0}& {0}\\ {0}& {1.65931985026082}& {0}\\ {0}& {0}& {3.29629655349925}{×}{{10}}^{{-16}}\end{array}\right]{,}\left[\begin{array}{ccc}{-0.294648032580691}& {-0.483670604727494}& {-0.824163383692134}\\ {-0.932505223882814}& {0.334015093825057}& {0.137360563948689}\\ {-0.208845742900333}& {-0.809009680547506}& {0.549442255794756}\end{array}\right]$ (3)