Rank–nullity theorem
id:
rank-nullity-theorem-202-11605824
title:
Rank–nullity theorem
text:
The rank–nullity theorem is a theorem in linear algebra, which asserts: the number of columns of a matrix M is the sum of the rank of M and the nullity of M; and
the dimension of the domain of a linear transformation f is the sum of the rank of f and the nullity of f. It follows that for linear transformations of vector spaces of equal finite dimension, either injectivity or surjectivity implies bijectivity.
brand slug:
wiki
category slug:
encyclopedia
description:
In linear algebra, relation between 3 dimensions
original url:
https://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem
date created:
date modified:
2024-04-18T16:26:55Z
main entity:
{"identifier":"Q303402","url":"https://www.wikidata.org/entity/Q303402"}
image:
{"content_url":"https://upload.wikimedia.org/wikipedia/commons/8/8f/Rank-nullity.svg","width":297,"height":300}
fields total:
13
integrity:
15