📂Functions

Radial Functions

Definition¹

If the function defined above by $\mathbb{R}^{n}$ satisfies the following, it is called radial.

$$ f(R\mathbf{x}) = f(\mathbf{x}) \text{ for all rotations } R $$

Explanation

Directly translated as a radial function, but hardly anyone calls it that. The function value depends only on the distance $\left| x \right|$ from the origin.

• In physics, it is often referred to as spherical symmetry. Examples include gravity, the electric field created by a point charge.
• In statistics, especially in spatial statistics, Isotropic Variogram is an example.