# Definition:Taxicab Norm

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## Definition

Let $\mathbf v = \tuple {v_1, v_2, \ldots, v_n}$ be a vector in $\R^n$.

The **taxicab norm** of $\mathbf v$ is defined as:

- $\displaystyle \norm {\mathbf v}_1 = \sum_{k \mathop = 1}^n \size {v_k}$

## Also known as

The **taxicab norm** is also known, particularly in American sources, as the **Manhattan norm**.

## Also see

### Generalizations

- Results about
**the taxicab norm**can be found here.

## Sources

- 2017: Amol Sasane:
*A Friendly Approach to Functional Analysis*... (previous) ... (next): $\S 1.2$: Normed and Banach spaces. Normed spaces