Q = v./max(v, [], 1);
Display it using format rat and you'll see it matches the form you wanted (modulo the fact that you swapped the second and third eigenvectors.) This won't change how Q is stored just how it's displayed. You can also check that Q is still a matrix of eigenvectors.
r = A*Q-Q*e % All elements should be small
If you turned on format rat before displaying r, you're going to need to switch to a different display format to see that the elements of r are small.
