Definition:Homogeneous Function

Definition
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 $n$ :
 * $\map f {\alpha \mathbf v} = \alpha^n \map f {\mathbf v}$

for all nonzero $\mathbf v \in V$ and $\alpha \in \GF$.

Zero Degree
A special case is when $n = 0$:

Real Number Space
Another special case is when $f: \R^2 \to \R$ is a real function of two variables.