---- > [!definition] Definition. ([[Schatten p-norm]]) > For $1 \leq p \leq \infty$, the **Schatten p-[[norm]]** of a [[matrix]] $A \in \mathbb{F}^{M \times N}$ is defined using the [[Lp-norm]] of its [[singular values]]: $\|A\|_{S,p}:=\left( \sum_{k=1}^{\min(M,N)} \sigma_{k}^{p} \right)^{1 / p}.$ > It is a [[matrix norm]] (i.e., is sub-multiplicative). ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```