- #1
aanabtawi
- 3
- 0
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,
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
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