Definition:Homogeneous Function/Zero Degree

Definition

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

Let $f: V \to W$ be a function from $V$ to $W$.

$f$ is a homogeneous function of degree zero if and only if:

$\map f {\alpha \mathbf v} = \alpha^0 \map f {\mathbf v} = \map f {\mathbf v}$