English: Compatibility of linear operators with scalar multiplication: A linear map ${\displaystyle f}$ is compatible with scalar multiplication, i.e. from ${\displaystyle w=\lambda v}$ follows ${\displaystyle f(w)=\lambda f(v)}$. This property can be condensed in ${\displaystyle f(\lambda v)=\lambda f(v)}$. For a non linear map this property might not hold. There might be ${\displaystyle \lambda \in K,v\in V}$ with ${\displaystyle f(\lambda v)\neq \lambda f(v)}$.