# Direct sum of subspaces

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)



## [Direct sum of subspaces](https://ocme.evemisslab.com/en/atlas/atlas-direct-sum/)

The sum of two subspaces is an internal direct sum when every vector in that sum has a unique decomposition; covering an ambient space is a separate spanning obligation.

atlas-direct-sum · canonical_mko

[Direct sum of subspaces](https://ocme.evemisslab.com/en/mko/mko-direct-sum/)

## Prerequisite nodes


- [Real vector subspace](https://ocme.evemisslab.com/en/atlas/atlas-vector-subspace/)
- [Set operations](https://ocme.evemisslab.com/en/atlas/atlas-set-operations/)
- [Linear independence and bases](https://ocme.evemisslab.com/en/atlas/atlas-linear-independence-basis/)