Homogeneity

algebra

Definition

Homogeneity

Let $V,W$ be vector spaces over a field $F$. A function $f:V\to W$ is homogeneous if scalar multiplication can be moved through $f$:

$$f(\lambda v)=\lambda f(v)\forall \lambda \in F,v\in V.$$

Homogeneity is one half of linearity, the other being additivity.