I'm trying to code up the Lanczos algorithm for eigenvalue approximation at the moment. I've seen on pages like this that the algorithm can't distinguish the eigenvectors if the dimension of the eigenspace is >1, but I don't understand why this makes it actually fail rather than just finish incompletely.
When I run tests the algorithm breaks because it ends up dividing by 0 when trying to find the orthonormal basis. Can anyone direct me to a proof / show my why it fails?