Schatten Norm

Definition

Let $A$ be an $m\times n$ matrix, then the Schatten norm of $A$ is defined as $||A|{|}_p={\left({\sum }_{i=1}^{\min \{m,n\}}{\sigma }_i^p\right)}^{1/p}$ where ${\sigma }_i$ is the $i$-th singularvalue of $A$

Facts

$p=1$: Nuclear Norm

$p=2$: Frobenius Norm $p=\infty$: Spectral Norm