Definition:Taxicab Metric/Real Vector Space

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

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


 * $\displaystyle d_1 \left({x, y}\right) := \sum_{i \mathop = 1}^n \left\vert {x_i - y_i}\right\vert$

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

Also see

 * Taxicab Metric on Real Vector Space is Metric