Definition:Taxicab Norm

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 for Until this has been finished, please leave {{Refactor}} in the code. New contributors: Refactoring is a task which is expected to be undertaken by experienced editors only. 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

• Taxicab Norm is Norm

• Results about the taxicab norm can be found here.

Generalizations

• Definition:P-Norm

Sources

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