I have this question and I think I can just use maths for (ii) X'Xa=lambda a XX'Xa=XX'(Xa)=lambda(Xa) And so if lambda and a are eigenvalues/eigenvectors of X'X then lambda and Xa will be eigenvalues/eigenvectors of XX'

Not sure if this is enough though, but my main problem is that I can't figure out why it is important that X is a centered data matrix. How does that change the eigenvalues? For the first part of the question I would just divide lambda by (n-1) but that just seems too simplistic

Thank you

I have this question and I think I can just use maths for (ii) X'Xa=lambda a XX'Xa=XX'(Xa)=lambda(Xa) And so if lambda and a are eigenvalues/eigenvectors of X'X then lambda and Xa will be eigenvalues/eigenvectors of XX'

Not sure if this is enough though, but my main problem is that I can't figure out why it is important that X is a centered data matrix. How does that change the eigenvalues? For the first part of the question I would just divide lambda by (n-1) but that just seems too simplistic