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!

Assume A is some diagnalizable matrix. Then, we can write A = P D$\ P^{-1}$. But, then, we can change the order of our eigenvalues along the diagnal in our matrix D, to produce some other matrix G. But, this corresponds to a change in the order of the eigenvectors in P, which again produces another matrix Q. So, in conclusion , we have A = Q G$\ Q^{-1}$. So, this implies we do NOT have uniqueness.
