#
# Numerical Mathematics and Computing, Fifth Edition
# Ward Cheney & David Kincaid
# Brooks/Cole Publ. Co.
# (c) 2003
#
# file:  sing_val_decomp
#
# Using Maple Linear Algebra package to determine
# the singular-value decomposition of the matrix A:

with(LinearAlgebra):
A := Matrix([[1, 3, -2],[2, 7, 5],[-2, -3, 4],[5, -3, -2]]);
U,Vt := SingularValues(A, output=['U','Vt']);
S:=SingularValues(A, output=['list']);
map(evalf[8],%);
Sig := DiagonalMatrix( S[1..3], 3, 4);
U.Sig.Vt;

with(LinearAlgebra):
A := Matrix([[1.,3.,-2.],[2.,7.,5.],
             [-2.,-3.,4.],[5.,-3.,-2.]]);
U,S,Vt := SingularValues(A, output=['U','S','Vt']);
DD := DiagonalMatrix( [S[1],S[2],S[3]],4,3);
B := evalf(U.DD.Vt, 6);