Rank of a vector bundle
= Rank of a vector bundle
{title2=$\operatorname{rank}E$}
= Vector bundle rank
{synonym}
The rank of a <vector bundle> at a point is the <dimension> of its fiber as a <vector space>. A <vector bundle trivialization> identifies nearby fibers with the same <vector space>, so this rank is locally constant. A rank-$r$ bundle has fibers of dimension $r$ everywhere.