# Real Hilbert space

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)



## [Real Hilbert space](https://ocme.evemisslab.com/en/atlas/atlas-real-hilbert-space/)

A real inner-product space is Hilbert when it is complete in the norm and metric induced by that same inner product.

atlas-real-hilbert-space · canonical_mko

[Real Hilbert space](https://ocme.evemisslab.com/en/mko/mko-real-hilbert-space/)

## Prerequisite nodes


- [Real inner-product space](https://ocme.evemisslab.com/en/atlas/atlas-real-inner-product-space/)
- [Inner-product-induced norm](https://ocme.evemisslab.com/en/atlas/atlas-inner-product-induced-norm/)
- [Norm-induced metric](https://ocme.evemisslab.com/en/atlas/atlas-norm-induced-metric/)
- [Complete metric space](https://ocme.evemisslab.com/en/atlas/atlas-complete-metric-space/)