(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

LetAbe anmxnmatrix with rank(A) = m < n. As far as the eigenvalues of [itex]A^{T}A[/itex] is concerned we can say that...

2. Relevant equations

3. The attempt at a solution

If eigenvalues exist, then

[itex]A^{T}A[/itex]x= λxwherex≠ 0.

The only thing I think I can show is that 0 is an eigenvalue:

If 0 is an eigenvalue for [itex]A^{T}A[/itex] then

[itex]A^{T}A[/itex]x= (0)xwherex≠ 0.

N(A) ≠ {0}, so Ax=0wherex≠ 0.

Therefore [itex]A^{T}(Ax) = 0[/itex] wherex≠ 0. So λ = 0 is an eigenvalue for [itex]A^{T}A[/itex].

Is there anything else that can be said about the eigenvalues for this matrix?

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# Homework Help: Eigenvalues of A transpose A

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