Compatibility of linear operators with scalar multiplication: A linear map f{\displaystyle f} is compatible with scalar multiplication, i.e. from w=λv{\displaystyle w=\lambda v} follows f(w)=λf(v){\displaystyle f(w)=\lambda f(v)}. This property can be condensed in f(λv)=λf(v){\displaystyle f(\lambda v)=\lambda f(v)}. For a non linear map this property might not hold. There might be λ∈K,v∈V{\displaystyle \lambda \in K,v\in V} with f(λv)≠λf(v){\displaystyle f(\lambda v)\neq \lambda f(v)}.
Own work
Stephan Kulla (User:Stephan Kulla)