Definition:Metric Induced by Norm

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Let $V$ be a normed vector space.

Let $\norm {\,\cdot\,}$ be the norm of $V$.

Then the induced metric or the metric induced by $\norm {\,\cdot\,}$ is the map $d: V \times V \to \R_{\ge 0}$ defined as:

$\map d {x, y} = \norm {x - y}$

Also known as

Induced metric is also known as induced distance.

Also see