Hi, I'm not sure if this is the right topic to post this in, so please let me know if there is another place I am better off asking. But for now, I have a set of vectors indexed by i, and my problem is that I am trying to find a proof that the function

is maximised when or when (because I only care about vectors with a norm of 1).

Just to clarify, I am sure that this is true, I just don't have a clean proof of it.