makes sense and satisfies all the properties of norm except that \|x\| = 0 does not imply x = 0 (such a functional is then called a semi-norm). We can produce an inner product space by considering the quotient W = V / \{x : \|x\| = 0\}. The sesquilinear form \langle \,\cdot\,, \,\cdot\, \rangle factors through W.
