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:
- $\displaystyle \norm {\mathbf v}_1 = \sum_{k \mathop = 1}^n \size {v_k}$
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.
Sources
- 2017: Amol Sasane: A Friendly Approach to Functional Analysis ... (previous) ... (next): $\S 1.2$: Normed and Banach spaces. Normed spaces