norm

p-norm of a vector is defined as: $||x|{|}_p=({\Sigma }_{i=1}^N||x_i|{|}^p{)}^{\frac{1}{p}}$

1. 0-norm: the number of non-zero components
2. 2-norm: Euclidian length
3. $\infty$-norm: the maximum of the components

when p-norm is used to measure distance:

1. 0-norm: number of changed components
2. 1-norm: Manhattan Distance
3. 2-norm: Eclidian distance
4. $\infty$-norm: maximum of changes