A homogeneuous [[Function|function]] $f$ of [[Arity]] $n$ is one such that if all arguments of $f$ are multiplied by some [[Scalar|scalar]] (of any [[Field]]), the multiplication can be 'factored out' as the multiplicative product between the scalar to the some power $k$, and the applied function $f$ on its arguments. $\huge f(sx_{1},sx_{2}, \dots,sx_{n}) = s^{k} $ This function can also be called a $k$-th ordered [[Homogeneous Function]].