I have a matrix $A=$$ \begin{bmatrix} 1 & 1 & 1 \\ 1 & -1 & 1 \\ 1 & 0 & -2 \\ \end{bmatrix} $ and I want to show that the columns of this matrix are the eigenvectors of $HH'$, where $H$ is the hypothesis matrix, and then find the associated eigenvalues.
My attempt: I wanted to use this form of the hypothesis matrix:
$H$=sum of squares matrix=$I_{k-1}|\frac{1}{k}J_{k-1}{J_k}'$ Because $A$ is a 3x3 matrix, $k$ would equal 4 I think. $J$ is a vector of 1's. I just don't know how to get from here to the eigenvectors/eigenvalues.