I am learning linear algebra (I know some introductory abstract algebra), and although I can imagine geometrically linear transformations from $\mathbb{R}, \mathbb{R}^2, \mathbb{R}^3$ to itself easily, I can't imagine a right picture of a linear transformation $\mathbb{F}_{p} \mapsto \mathbb{F}_p$ or $\mathbb{F}_{p^2} \rightarrow \mathbb{F}_{p^2}$ etc (over the field $\mathbb{F}_p$)
Also how you think about $\mathbb{C}^n \mapsto \mathbb{C}^n$ over the field $\mathbb{C}$, where $n > 1$ ? I have a hard time imagining even $\mathbb{R}^3$, so I can't picture four dimensional $\mathbb{C}^2$ at all.
What's the right mental imagery to imagine about such mappings ?