matrix m:
1.000000 0.000000 0.000000 0.000000 0.000000 
0.000000 2.000000 0.000000 0.000000 0.000000 
0.000000 0.000000 3.000000 0.000000 0.000000 
0.000000 0.000000 0.000000 4.000000 0.000000 
0.000000 0.000000 0.000000 0.000000 5.000000 

m in random representation:
3.302687 -0.026361 -0.296448 -1.380532 -0.750046 
-0.026361 2.943266 1.298046 0.462775 0.389657 
-0.296448 1.298046 2.924602 -0.154699 0.071087 
-1.380532 0.462775 -0.154699 2.422599 0.251726 
-0.750046 0.389657 0.071087 0.251726 3.406846 

eigenvalues after 6 sweeps
1.000000 
2.000000 
3.000000 
4.000000 
5.000000 

eigenvectors v:
-0.466290 -0.393527 0.318024 0.400923 -0.604840 
0.449977 -0.546797 -0.026063 0.590337 0.386467 
-0.419906 0.561040 -0.120867 0.629760 0.312580 
-0.619601 -0.481024 -0.372665 -0.264329 0.419478 
-0.140954 -0.000637 0.862956 -0.155867 0.459504 

v^Tmv:
1.000000 0.000000 0.000000 0.000000 0.000000 
0.000000 2.000000 -0.000000 -0.000000 0.000000 
0.000000 -0.000000 3.000000 -0.000000 0.000000 
0.000000 -0.000000 -0.000000 4.000000 0.000000 
0.000000 -0.000000 0.000000 0.000000 5.000000