I am using SVD to solve a homogeneous system of $N$ linear equations in $12$ variables, where $N \gg 12$, in the least-squares sense. In order to determine the null-space of the $N \times 12$ matrix, I need to pick out the eigenvalues which are zero. But in a numerical solution the eigenvalues are near zero, here an example of the $12$ eigenvalues for a sample $N \times 12$ matrix:
S = [ 15.2158 5.96262 5.53325 3.27387 3.03468 2.84257 0.683411 0.625499 0.20319 0.136146 0.0276132 0.00103614 ]
Because I am using known input/output pairs, I know that
[ 0.0276132 0.00103614 ]
are the two "zero" eigenvalues. However, in the general case, where does one put the threshold below which the eigenvalue is considered zero, especially when eigen values do not have a unit?