If $v_1,v_2...v_n$ are eigenvectors of an $n\times n$ matrix, is it possible to find $\sum_{i=0}^{n} v_i$ without explicitly finding the eigen vectors?

All the vectors are normalized to 1 and $+1$ or $-1$ in front of it doesn't matter.

It is most probably not possible. I couldn't derive any expression and also couldn't find anything online. So, is it possible?