Category:Definitions/Homogeneous Functions

This category contains definitions related to Homogeneous Functions.
Related results can be found in Category:Homogeneous Functions.

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 $n$ if and only if:

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

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