Definition:Taxicab Norm

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

• Taxicab Norm is Norm

Generalizations

• Definition:P-Norm

• 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