\begin{definition}[Definition:Homogeneous Function]
Let $V$ and $W$ be two vector spaces over a field $\GF$.
Let $f: V \to W$ be a function from $V$ to $W$.
Then $f$ is '''homogeneous of degree $n$''' {{iff}}:
:$\map f {\alpha \mathbf v} = \alpha^n \map f {\mathbf v}$
for all nonzero $\mathbf v \in V$ and $\alpha \in \GF$.
\end{definition}