# Definition:Homogeneous Function/Degree

Let $V$ and $W$ be two vector spaces over a field $F$.
Let $f: V \to W$ be a homogeneous function of degree $n$ from $V$ to $W$:
$f \left({\alpha \mathbf v}\right) = \alpha^n f \left({\mathbf v}\right)$
for all nonzero $\mathbf v \in V$ and $\alpha \in F$.
The element $n \in \N$ is the degree of $f$.