Lineare Abbildungen

$$f:\quad\begin{aligned}\displaystyle&\displaystyle V\to W\\ \displaystyle&\displaystyle v\mapsto f(v)\end{aligned}$$

$$\begin{aligned}\displaystyle&\displaystyle\text{(i)}&\displaystyle&\displaystyle f(v+u)=f(v)+f(u)&\displaystyle&\displaystyle\forall\,v,u\in V.\\ \displaystyle&\displaystyle\text{(ii)}&\displaystyle&\displaystyle f(\lambda\cdot v)=\lambda\cdot f(v)&\displaystyle&\displaystyle\forall\,v\in V,\enspace\forall\,\lambda\in{\mathbb{R}}.\end{aligned}$$