Computing eigenvector corresponding to dominant eigenvector.

Question

My question is, why does the eigenvector have to be a unit vector?

Please see the code below, every time the eigenvector is gained after normalization, which I don't understand.

Thank you

Answer 1

An eigenvector doesn't have to be a unit vector. But in an iterative process such as this, if you don't normalize it you're likely to have your vector either converge to $0$ or "blow up" with norm going to $\infty$, both of which are bad.