---- > [!definition] Definition. ([[inner product on a vector bundle]]) > Let $E \xrightarrow{\pi} B$ be a [[vector bundle]] and $k$ a [[field]]. An **inner product** on $E$ is a [[Whitney sum of vector bundles|map]] $\langle -,- \rangle : E \oplus E \to k $ which restricts to an [[inner product]] over each fiber. ^definition ---- #### [[Whitney sum of vector bundles]] ---- #### 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 > ```