I've never run into a singular matrix before, so bear with me.
I have a complex non-symmetric matrix (about 1000 x 1000) that I know has a couple zero eigenvalues. It isn't guaranteed to be diagonalizable, but when I pass it to ZGEEV, I see no apparent problems. I use all the eigenpairs for later analysis, but I am unsure if I am 'allowed' to do this.
Can I trust the results of ZGEEV for computing the eigenvalues and eigenvectors when my matrix is singular, or is there a better way to compute these eigenpairs?
As far as I can tell, the eigenvectors are not the trivial solutions. Is ZGEEV actually stable for computing Ax = 0?