# Definition:Taxicab Norm

Jump to navigation
Jump to search

This page has been identified as a candidate for refactoring of advanced complexity.In particular: Find the most abstract sequence where this definition makes sense, which is probably that same Banach space that the original Definition:P-Norm was defined forUntil this has been finished, please leave
`{{Refactor}}` in the code.
Because of the underlying complexity of the work needed, it is recommended that you do not embark on a refactoring task until you have become familiar with the structural nature of pages of $\mathsf{Pr} \infty \mathsf{fWiki}$.To discuss this page in more detail, feel free to use the talk page.When this work has been completed, you may remove this instance of `{{Refactor}}` from the code. |

## 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:

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

## Also known as

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

## Also see

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

### Generalizations

## Sources

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