Definition:Metric Induced by Norm

Definition
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:


 * $d \left({x, y}\right) = \left\Vert{x - y}\right\Vert$

Also known as
Induced metric is also known as induced distance.

Also see

 * Metric Induced by Norm is Metric