Why bracket? The reason is that there is not only ket vectors |v> but also functionals <u| that can be applied to them, which will look like this <u|v>. So ther

Why bracket? The reason is that there is not only ket vectors |v> but also functionals <u| that can be applied to them, which will look like this <u|v>. So there are brackets around the construct. Think <bra|ket> if you like.