Complexification of a real vector bundle
= Complexification of a real vector bundle
{title2=$E\otimes_{\mathbb R}\mathbb C$}
Complexification replaces each fiber of a real <vector bundle> by its <tensor product> with $\mathbb C$ over $\mathbb R$. The <complexification of a real vector bundle> of rank one is a <complex line bundle>. For the <tautological bundle> over <Real projective space>, this <complex line bundle> squares to the <trivial vector bundle>.