Transition function of a vector bundle
= Transition function of a vector bundle
{title2=$g_{ij}:U_i\cap U_j\to\operatorname{GL}_r$}
= Transition functions of a vector bundle
{synonym}
Two local frames of a <vector bundle> differ on their overlap by an invertible matrix-valued function. These functions satisfy the <Čech cocycle condition>. For a <holomorphic vector bundle> they are <holomorphic>, and for a <holomorphic line bundle> they are scalar holomorphic units.