I wonder if there is any trick to calculate the eigenvalue and eigenvectors for the all-1 matrix, namely $A=% \begin{bmatrix} 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 1 & 1% \end{bmatrix}% $
More over, suppose I have a matrix which has a form $A=U\cdot V^{T}$, that U and V are low rank, but not necessarily orthogonal basis, is there any trick that I can quickly get the eigenvalue?
Thanks a lot.