(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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Eigenvalues of A transpose A

**Physics Forums | Science Articles, Homework Help, Discussion**