A complex vector bundle is a vector bundle 
whose fiber
bundle 
is a complex vector space. It is not necessarily
a complex manifold, even if its base
manifold 
is a complex manifold. If a complex vector bundle
also has the structure of a complex manifold,
and 
is holomorphic, then it is called a holomorphic vector bundle.
Complex Vector Bundle
See also
Bundle, Complex Vector Space, Holomorphic Vector Bundle, Manifold, Vector SpaceThis entry contributed by Todd Rowland
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Rowland, Todd. "Complex Vector Bundle." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ComplexVectorBundle.html