L1 norm: Difference between revisions

Revision as of 18:40, 11 May 2014

Definition

Suppose $n$ is a positive integer. The $L^{1}$ -norm, denoted $| \cdot |_{1}$ , is a function from $R^{n}$ to $R$ defined as:

$| x |_{1} = \sum_{i = 1}^{n} | x_{i} |$

Definition in terms of the signum vector function

The $L^{1}$ -norm $| x |_{1}$ can be defined as the dot product $\vec{s g n} (\vec{x}) \cdot \vec{x}$ where $\vec{s g n}$ denotes the signum vector function.

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 <math>\| x \|_1 = \sum_{i=1}^n |x_i|</math>
+===Definition in terms of the signum vector function===
+The <math>L^1</math>-norm <math>\| x \|_1</math> can be defined as the [[dot product]] <math>\vec{sgn}(\vec{x}) \cdot \vec{x}</math> where <math>\vec{sgn}</math> denotes the [[signum vector function]].