Prove rank of (A^t)A equals rank of A

pcming · Oct 5, 2006

I can't find out how to prove this question. Can anyone help?

Let A be an n x m matrix of rank m, n>m. Prove that (A^t)A has the same rank m as A.

Where A^t = the transpose of A.

I seen someone else have asked the question before and had got the answer. However I can't understand it. Hope someone can give me a more detail suggestion. Thanks!

nocturnal · Oct 6, 2006

You need to show some work first. You say you've seen a proof already but are having trouble understanding it, well what is the proof and which part is giving you trouble. There is more than one way to do it.

It's a good idea to attempt the proof yourself first without looking at the answer.

Edit: I just noticed the other thread you're talking about which has the answer you don't understand, and which ironically was written by me along ways back

I responded to your question in that thread.

Prove rank of (A^t)A equals rank of A

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