Matrix p-Norm

Definition

Let $A$ be an $m\times n$ matrix, then the matrix p-norm of $A$ is defined as $||A|{|}_p=\underset{\mathbf{x}\ne 0}{\sup }\frac{||A\mathbf{x}|{|}_p}{||x|{|}_p}=\underset{||\mathbf{x}|{|}_p=1}{\max }||A\mathbf{x}|{|}_p$

Facts

When $p=2$, the norm is a Spectral Norm.