This is late but double bar [imath]||x||[/imath] means the norm, or the length of a vector. Angle brackets [imath]<x, y>[/imath] means the inner product. The most familiar examples of these is the Euclidean norm and the dot product, respectively. There's a lot of theory associated with these operations, some of it is not very simple, but is needed to extend some cool linear algebra tricks to problems involving functions instead of just problems involving vectors and matrices.