Middle terms...
Are not always zero for the eigenvalues 5 and -2. The P matrix should be something like
0.7071 -0.6000 0 0 0 1.0000 0.7071 0.8000 0
According to MATLAB (the first column is likely sqrt(2)/2). This gives the diagonal matrix diag(5,-2,3).
CarmenBruni (talk)