I'm self taught though, so please bear with any questions i have. One side of the cauchy schwarz innequality (CSI, nice acronym) is l u.v l Firstly what's the difference between ll u ll and l u l . I thought the norm was the length. Also, what does it mean by the length of the dot product of u and v? I thought the dot product was a number itself, and not a tuple or something.