# Definition:Chebyshev Distance/Real Vector Space

## Definition

Let $\R^n$ be an $n$-dimensional real vector space.

The Chebyshev distance on $\R^n$ is defined as:

$\ds \map {d_\infty} {x, y}:= \max_{i \mathop = 1}^n \set {\size {x_i - y_i} }$

where $x = \tuple {x_1, x_2, \ldots, x_n}, y = \tuple {y_1, y_2, \ldots, y_n} \in \R^n$.

### Real Number Plane

This metric is usually encountered in the context of the real number plane $\R^2$:

The Chebyshev distance on $\R^2$ is defined as:

$\map {d_\infty} {x, y}:= \max \set {\size {x_1 - y_1}, \size {x_2 - y_2} }$

where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.

## Also see

• Results about the Chebyshev distance can be found here.