Definition:Taxicab Metric

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

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

Let the metric $$d_1$$ be imposed on $$\reals^n$$ such that $$d_1 \left({x, y}\right) = \sum_{i=1}^n \left|{x_i - y_i}\right|$$.

The metric $$d_1$$ is called the taxicab metric.

The Taxicab Metric is a Metric.