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 $\displaystyle \{ \mathbf{a}_i \}$ indexed by i, and my problem is that I am trying to find a proof that the function

$\displaystyle \sum_i (\mathbf{a}_i\cdot\mathbf{b})^2$ is maximised when $\displaystyle \mathbf{b}=\sum_i \mathbf{a}_i$ or when $\displaystyle \mathbf{b} \parallel \sum_i \mathbf{a}_i$ (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.