Interpretation of the eigenvalues of the inverse Hessian in a KLT tracker
Think of them as 2D smoothness terms.
The smoother the patch, the lower the matrix rank and the closer the matrix is to being singular.  

On an straight edge (not a corner), just one eigenvalue will be large.
On a corner both will be large.  

Using eigenvalues means that the angle of the edge is not a factor, and at any angle, an edge will give just one large e.v.