# Determining whether limit goes to inifnity exists for matrices in Jordan canonical form

Recently in class, we covered the Jordan canonical form of matrices. I'm just confused as to when the limit $$\lim_n\rightarrow\infty$$ exists for certain matrices expressed in such a form - if someone could refer me to a source which covers examples of the above (or alternatively provide a couple of examples), I'd really appreciate it.

Thanks!