I have a large sparse matrix corresponding to a system of master equations for a continuous-time Markov chain. It's approximately $500,000 \times 500,000$, with a density of around $10^{-6}$.
Is there a quick(er) way to calculate just the eigenvector corresponding to the $\lambda=0$ eigenvector, (I'm currently using eigs in matlab) particularly for when I need to do this for larger matrices?