I'm trying to prove that the null space of A'A is the null space of A, this is what I have so far,(adsbygoogle = window.adsbygoogle || []).push({});

1) A'Ax=0, non trivial solutions are a basis for the null space of A'A

2) x'A'Ax=0

3) (Ax)'Ax=0

4) Since (Ax)'A is a linear combination of the col's of A, we see that the null space of A can be written as a linear combination of the basis for the null space of A'A.

Therefore, they have the same null space.

--> Is this proof valid? I am unsure if argument 4 holds ground, but it seems to make sense to me =P

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# A'A and A have the same null space

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