I'm a physics major. As such, I have come across several situations in my studies that require the use of eigenvectors and eigenvalues. Whenever I have to use this method, I've been told to. I do not have a complete understanding of eigenvectors and values and am wondering how you would spot a situation where you would need to use them. For example, if I wanted to know when or where the rate of change of something was 0, I would take a derivative, set it equal to zero, then solve for some variable. What sort of situation would I look for (in general) that would make me say "Hey! I need to find some eigenvectors here."? Thanks.