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.