Definition:Homogeneous Function/Degree

Definition
Let $V$ and $W$ be two vector spaces over a field $F$.

Let $f: V \to W$ be a homogeneous function 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 $\alpha \in F$ is the degree of $f$.