Q:

Reconstruct a matrix from given eigenvalues

I wanted to know how can I reconstruct a matrix just from its given eigenvalues. 
I'm really sorry, cause after working on it for 3 days, I haven't any idea about how to do this, therefore I haven't anything useful to share. 
NOTE:
I know how to reconstruct a matrix from given eigenvalues and eigenvectors. 

A:

No, any matrix $U^{-1}AU$ has the same eigenvalues and Jordan normal form as $A$.  In fact, one can say that the Jordan normal form is the standard representative of these classes of conjugate matrices.