$\mathbb{R}$-linear and $\mathbb{C}$-linear What does it mean for a map $\phi$ to be $\mathbb R$-linear or $\mathbb{C}$-linear? I have tried to look for this definition on Google but I cannot find it.

A linear map is a map between vector spaces (over the same field) that preserves the vector operations of scalar multiplication and vector sum. The names $\mathbb{R}$-linear and $\mathbb{C}$-linear are just a reminder of what field we are looking at.
