# 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

### Generalizations

• Results about the taxicab norm can be found here.