Definition:Taxicab Metric/Real Vector Space

Definition
Let $\R^n$ be a real vector space.

The taxicab metric on $\R^n$ is defined as:


 * $\ds \map {d_1} {x, y} := \sum_{i \mathop = 1}^n \size {x_i - y_i}$

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

Also see

 * Taxicab Metric on Real Vector Space is Metric