So, it provides a modicum of organization (I know exactly where to look for SparseVector/DenseVector operations.) 

Also, I don't know if this was relevant for here, but if A is a subtrait of B, and there is an implicit in A and an implicit in B that both match, it will prefer A. So I'll use the extends as a kind of partial order for implicit search. Jason Zaugg (@retronym) recently posted something about putting more specialized implicits in trait below less explicit ones in order to speed up compilation, I think it only applies in 2.11 and higher.