The L1 Mat-1.1010 -course here has taught me the linearity conditions $f(a x)=a f(x)$ and $f(a+b)=f(a)+f(b)$. I want to generalize it, some quite irrelevant slow investigation here.
It requires time to verify statements like below, source here.
According to Wikipedia here, $Ly=f$ and
but I cannot see this kind of statements fast, unless going through the conditions one-by-one. So are there fast ways to check whether some differential is linear or not?