p-norm

Let $p\ge 1$ be a real number,  The p-norm (also called $l_p$-norm) of vector $x=(x_1,...,x_n)$ is

$$||x|{|}_p:=(\sum _{i=1}^n|x_i{|}^p{)}^{1/p}$$

• For p = 1 -> taxicab norm
• For p = 2 -> Euclidean norm
• For p = $\mathrm{\infty }$ -> $ma{x}_i|x_i|$