Rank of a linear transformation

[matqkks]

Is there a short and simple proof of the Nullity - Rank Theorem which claims that if T: U->V is a linear transformation then rank(T)+Nullity(T)=n where n is the n dimension vector space U.

[chiro]

Hey matqkks.

Have you checked the wikipedia page?

http://en.wikipedia.org/wiki/Rank%E2%80%93nullity_theorem

The second proof on that page looks ok. Hopefully it should answer your question.