qNorm: Let X
be a
vector space. ||•|| is a norm if
• (i) ||x||³0 (positivity);
• (ii) ||x||=0 if and only if x = 0 (positive
definiteness);
• (iii) ||ax||=|a| ||x|| for any scalar a (homogeneity);
• (iv) ||x+y||£||x||+||y|| (triangle
inequality)
• for any xÎ X and yÎ X.
• Let xÎ Cn. Then we define the vector p-norm of x as