a random real symmetric matrix A:
  0.680 -0.211  0.566  0.597
 -0.211  0.823 -0.605 -0.330
  0.566 -0.605  0.536 -0.444
  0.597 -0.330 -0.444  0.108
matrix A after jacobi (should be diagonal):
 -0.786 -0.000  0.000 -0.000
 -0.000  0.479  0.000  0.000
  0.000  0.000  0.800 -0.000
 -0.000  0.000 -0.000  1.655
matrix V^T*A*V (should equal A after jacobi):
 -0.786 -0.000  0.000  0.000
 -0.000  0.479 -0.000  0.000
  0.000  0.000  0.800 -0.000
  0.000  0.000 -0.000  1.655
matrix V*D*V^T (should equal original A):
  0.680 -0.211  0.566  0.597
 -0.211  0.823 -0.605 -0.330
  0.566 -0.605  0.536 -0.444
  0.597 -0.330 -0.444  0.108
matrix V^T*V (should equal identity matrix):
  1.000 -0.000 -0.000  0.000
 -0.000  1.000 -0.000 -0.000
 -0.000 -0.000  1.000  0.000
  0.000 -0.000  0.000  1.000