Is a diagonalization of a matrix unique? I was solving problems of diagonalization of matrices and I wanted to know if a diagonalization of a matrix is always unique? but there's nothing about it in the books nor the net. 
I was trying to look for counter examples but I found none.
Any hint would be much appreciated
Thanks!

The diagonal matrix is unique up to a permutation of the entries (assuming we use a similarity transformation to diagonalize). If we diagonalize a matrix $M = U\Lambda U^{-1}$, the $\Lambda$ are the eigenvalues of $M$, but they can appear in any order.
