SVD Only With Matrix of Full Rank?

[Han]

The svd2 program gives:

Code:


m1:=[ [8 ,2 ,2 ,-6], [5, 0, 3, -4], [-2 ,-3 ,3 ,1], [2 ,3 ,-3, -1], [4, 6 ,-6 ,-2] ];
svd2(m1);

{
  [ [−0.663425500474,  −0.457402727004, −0.592156525464,    3.5904651478e−13,  −8.40216785036e−13],
    [−0.364141989004,  −0.493987842429,  0.789542033952,    5.44011574989e−13,  4.52975068342e−13],
    [ 0.266854272705,  −0.301871594352, −6.57951694972e−2,  0.581376370892,     0.703800290354],
    [−0.266854272705,   0.301871594352,  6.57951694972e−2, −0.573305362697,     0.710390240949],
    [−0.53370854541,    0.603743188705,  0.131590338991,    0.577340866795,    −3.29497529792e−3] ],

  [ 14.1250482296, 9.82257667368, 6.3812064393e−12, 1.79164513489e−23],

  [ [−0.731350792814,   −0.433996954204,   0.168785260197,  0.498281243408],
    [−0.255197997351,    0.460050696925,  −0.797189774107,  0.296168537264],
    [−0.628778070935,    0.390531480179,   0.186669569957, −0.645970411205], 
    [−6.81038729371e−2, −0.668943318219,  −0.548775429161, −0.496711413046] ]
}

for U, S, and V respectively, where U*diag(S)*V = original matrix. The difference between U*diag(S)*V and m1 is

Code:

[ [−1.45803369378e−11, −2.13162820728e−12, −1.79767312147e−12,  4.64694949187e−11],
  [−5.17275111633e−12,  9.8119794999e−12,  −3.41060513165e−12,  2.09752215596e−11],
  [ 8.17124146124e−13,  4.41957581643e−12, −2.30215846386e−12, −3.47100126419e−12],
  [−8.17124146124e−13, −4.41957581643e−12,  2.30215846386e−12,  3.47100126419e−12],
  [−4.13535872212e−12, −4.32009983342e−12, −3.24007487507e−12,  9.85522774499e−12] ]