Original sentence: For all the problems below, assume that we are given (in addition to other more specific inputs) a basis for the vector space V and a norm N (often L2)
Edited sentence: For all the problems below, assume that we are given (in addition to other more specific inputs) a basis for the vector space V and a norm N.However, other norms (such as Lp) are also considered and show up in variety of results.The norms usually considered are L2