 Frame of a vector bundle (source code)

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= Frame of a vector bundle
{title2=$e=(e_1,\ldots,e_r)$}

= Local frame
{synonym}

= Bundle frame
{synonym}

A frame over an open set $U$ is a list of smooth sections $e_1,\ldots,e_r$ of a rank-$r$ <vector bundle> whose values form a basis in every fibre over $U$. It is equivalent to a <vector bundle trivialization> by $(x,v)\mapsto\sum_a e_a(x)v^a$. Two local frames differ by a smooth map $g:U\to\mathrm{GL}(r)$, written $e'=eg$.

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