How does Mathematica assign the eigenvectors to a singular matrix? For example, the three-dimensional null matrix
mat = {{0, 0, 0}, {0, 0, 0}, {0, 0, 0}}
has the eigenvectors
In[4]:= Eigenvectors[mat]
Out[4]= {{0, 0, 1}, {0, 1, 0}, {1, 0, 0}}
What algorithm is used to order these degenerate eigenvectors?
I ask because in other situations it is not always anticipated that there will be degeneracies and hence singularities of the matrix.
