Definition:Homogeneous


 * Algebra:
 * Homogeneous quadratic equation: a quadratic equation in two variables in the form $a x^2 + h x y + b y^2 = 0$


 * Analytic Geometry:
 * Homogeneous: a line or plane is homogeneous if it contains the origin.
 * Homogeneous Cartesian coordinates: such that $\tuple {x, y}$ is expressed as $\tuple {X, Y, Z}$ where $x = \dfrac X Z$ and $y = \dfrac Y Z$.


 * Polynomial Theory
 * Homogeneous Polynomial


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


 * Differential Equations:
 * 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.


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


 * Metric Spaces:
 * Homogeneous: Another term for translation invariant.


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


 * Mathematical Models:
 * Homogeneous:

Also see

 * Definition:Homogenization