Do you understand the following:

To be able to diagonalise an nxn matrix, it has to have n linearly independent eigenvectors.

For a matrix to be diagonalizable it does not necessarily have to have n different eigenvalues. 

If v₁, v₂, v₃, ... are linearly independent eigenvectors with corresponding eigenvalues  l₁, l₂, l₃, ... , respectively. To make up the matrix D we can add the eigenvalues in any order. However, when we then build the corresponding diagonalizing matrix T we have to use the corresponding eigenvectors in the same order.

For a matrix to be diagonalizable is a good thing :)