An homogeneous function of grade $k$ is a function $f$:
$f(x_1,...,x_n):{\mathbb{R}}^n\to \mathbb{R}$
such that, given $\alpha ,k\in \mathbb{R}$,
$f(\alpha x_1,...,\alpha x_n)={\alpha }^{k}f(x_1,...,x_n)$