Embeddings of Schatten Norms with Applications to Data Streams

Yi Li, David P. Woodruff

Given an $n\times d$ matrix $A$, its Schatten-$p$ norm, $p\ge 1$, is defined as $\Vert A{\Vert }_p={\left({\sum }_{i=1}^{\text{rank}(A)}{\sigma }_i(A{)}^p\right)}^{1/p}$, where ${\sigma }_i(A)$ is the $i…