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:

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


Also known as

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


Also see


Generalizations

  • Results about the taxicab norm can be found here.


Sources