SVD Only With Matrix of Full Rank?

[parisse]

I have modified the implementation in Xcas. It will handle 0 as singular value.

Code:


m1:=[ [8 ,2 ,2 ,-6], [5, 0, 3, -4], [-2 ,-3 ,3 ,1], [2 ,3 ,-3, -1], [4, 6 ,-6 ,-2] ];
u,s,q:=SVD(m1);
m:=u*[op(diag(s)*trn(q)),[0$4]]

Then m is equal to m1 up to numerical errors, but the quick and dirty algorithm I' using is unfortunately far from optimal for numerical stability if 0 is a singular value, especially here where it has multiplicity >1.