---- > [!definition] Definition. ([[unitarily invariant vector norm]]) > A vector [[norm]] $\|\cdot\|$ on [[vector space]] $V$ is called **unitarily invariant** if for every [[linear isometry]] $U \in \text{End}(V)$ $\|Ux\|=\|x\|.$ > [!basicexample] > - [[group-invariant function#^465067|euclidean norm is unitarily invariant]] ---- #### ---- #### 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 > ```