# Norm-induced metric

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Norm-induced metric](https://ocme.evemisslab.com/en/atlas/atlas-norm-induced-metric/)

On the same real normed vector space, taking the norm of a vector difference defines a metric whose axioms follow universally from the norm axioms.

atlas-norm-induced-metric · canonical_mko

[Norm-induced metric](https://ocme.evemisslab.com/en/mko/mko-norm-induced-metric/)

## Prerequisite nodes


- [Real normed vector space](https://ocme.evemisslab.com/en/atlas/atlas-real-normed-vector-space/)
- [Metric space](https://ocme.evemisslab.com/en/atlas/atlas-metric-space/)
- [Plane vectors in a fixed basis](https://ocme.evemisslab.com/en/atlas/atlas-vector/)
- [Function mapping](https://ocme.evemisslab.com/en/atlas/atlas-function-mapping/)