Definition:Homogeneous


 * Homogeneous (Analytic Geometry): a line or plane is homogeneous if it contains the origin.


 * Homogeneous Linear Equations: a system of simultaneous equations which are all equal to zero.


 * Definition:Homogeneous Polynomial


 * Homogeneous function: a function $f: V \to W$ between two vector spaces over a field $F$ is homogeneous of degree $n$ $\map f {\alpha \mathbf v} = \alpha^n \map f {\mathbf v}$ for all nonzero $\mathbf v \in V$ and $\alpha \in F$.
 * Also see: homogeneous real function.


 * Homogeneous differential equation: a first order ordinary differential equation of the form $\map M {x, y} + map N {x, y} \dfrac {\d y} {\d x} = 0$, where both $M$ and $N$ are homogeneous functions.


 * Homogeneous (Model Theory): A concept in model theory.


 * Homogeneous (Metric Spaces): Another term for translation invariance.


 * Homogeneous (Physics): of a body, the same all the way through.

Also see

 * Definition:Homogenization