Linear operators are compatible with addition, i.e. the sum v3=v1+v2{\displaystyle v_{3}=v_{1}+v_{2}} is maintained by the linear operator f{\displaystyle f} via f(v3)=f(v1)+f(v2){\displaystyle f(v_{3})=f(v_{1})+f(v_{2})}. This property can be condensed in f(v1+v2)=f(v1)+f(v2){\displaystyle f(v_{1}+v_{2})=f(v_{1})+f(v_{2})}.
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Stephan Kulla (User:Stephan Kulla)