In his book, Daniel Huybrechts define the complexified tangent bundle as: $T_{\mathbb C}U:= TU \otimes \mathbb C$.
But I don't understand this tensor product, I understand what $T_xU \otimes \mathbb C$ is, but here $TU$ is a vector bundle on $U$, while $\mathbb C$ is not, but the definition of tensor product between vector bundles I found on Wikipedia require that the both vector bundles are over the same space.
Can anyone help me please ?