Untitled

We verify some of the fundamental SVD properties using the built-in MATLAB command svd.

A = vander(1:5);
A = A(:,1:4)
A = 
     1     1     1     1
    16     8     4     2
    81    27     9     3
   256    64    16     4
   625   125    25     5

[U,S,V] = svd(A);
norm(U'*U - eye(5))
ans = 
   1.4850e-15

norm(V'*V - eye(4))
ans = 
   1.2551e-15

sigma = diag(S)
sigma = 
   6.9584e+02
   1.8205e+01
   1.6989e+00
   2.1202e-01

[ norm(A) sigma(1) ]
ans = 
   6.9584e+02   6.9584e+02

[ cond(A) sigma(1)/sigma(4) ]
ans = 
   3.2820e+03   3.2820e+03