# Rank-nullity theorem

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)



## [Rank-nullity theorem](https://ocme.evemisslab.com/en/atlas/atlas-rank-nullity-theorem/)

A linear map T:V→W with finite-dimensional source satisfies dim(V)=dim(ker T)+rank(T).

atlas-rank-nullity-theorem · canonical_mko

[Rank-nullity theorem](https://ocme.evemisslab.com/en/mko/mko-rank-nullity-theorem/)

## Prerequisite nodes


- [Kernel of a linear map](https://ocme.evemisslab.com/en/atlas/atlas-linear-map-kernel/)
- [Image of a linear map](https://ocme.evemisslab.com/en/atlas/atlas-linear-map-image/)
- [Matrix rank](https://ocme.evemisslab.com/en/atlas/atlas-matrix-rank/)
- [Dimension of a finite-dimensional vector space](https://ocme.evemisslab.com/en/atlas/atlas-vector-space-dimension/)