L-pq Norm

Definition

$L_{pq}$ norm is an entry-wise matrix norm. $||A|{|}_{p,q}={\left(\sum _{i=1}^n{\left(\sum _{j=1}^n|a_{ij}{|}^p\right)}^{q/p}\right)}^{1/q}$ where $p,q\ge 1$

Facts

When $p=q=1$, the norm is the sum of the absolute values of every entry and is called a matrix $L_1$ norm.