= Holomorphic splitting of transition functions on a trivial bundle
{title2=$F_{\alpha\beta}=H_\beta H_\alpha^{-1}$}
For a holomorphically <trivial vector bundle>, choose a global <holomorphic> <bundle frame>. Let the columns of $H_\alpha$ be the coordinates of that frame in the prescribed frame over $U_\alpha$. If fiber coordinates transform as $s_\beta=F_{\alpha\beta}s_\alpha$, then $H_\beta=F_{\alpha\beta}H_\alpha$. Each <matrix> is <holomorphic> and invertible, giving the displayed splitting. Conversely such <matrices> give agreeing global <holomorphic sections> forming a frame. Topological triviality alone does not supply this conclusion.
// Destination: electromagnetism.bigb
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