If $f(g(x)) = g(f(x))$ whats the name of the properties on $f$ and $g$
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Isnt commutativity $f(x,y) = f(y,x)$? – iluvAS May 17 '20 at 06:20
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Maybe i can give more context, it comes from this lecture at 13:30 the equation is the property that a variable is linear using the Linearity operator $L$, $L u = 0$ and the property that $L$ must have is $L(a u) = a L u$, im trying to give a name to this property. – iluvAS May 17 '20 at 06:28
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You can say that $f$ and $g$ commute. "Commuting" makes sense with respect to a given operation. In your case, it is the operation $\circ$ of composition, and $f(g(x)) = g(f(x))$ for all $x$ is also written just as $f\circ g = g \circ f$. Writing $f(x,y) =f(y,x)$ means that $f$ is symmetric, which is something else.
Ivo Terek
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