test_eigen.py
a1=
[[ 0.5         0.33333333  0.25        0.2       ]
 [ 0.33333333  0.25        0.2         0.16666667]
 [ 0.25        0.2         0.16666667  0.14285714]
 [ 0.2         0.16666667  0.14285714  0.125     ]]
lambda=
[  9.77556281e-01   6.22678235e-02   1.82125544e-03   2.13065856e-05]
vectors=
[[ 0.69524173  0.66277303  0.2722824  -0.05686079]
 [ 0.50244805 -0.18857925 -0.7387851   0.40765231]
 [ 0.395998   -0.4630991  -0.04915549 -0.79139658]
 [ 0.32767436 -0.55741278  0.61452633  0.45197113]]
 
det|a - lambda*I| should be near zero
check eig =  0.977556281151 , det =  8.23444432696e-17
check eig =  0.0622678234923 , det =  3.60910979306e-21
check eig =  0.00182125543747 , det =  -5.25933318744e-22
check eig =  2.1306585633e-05 , det =  -3.79817496756e-21
 
sum of abs of dot product of all v should be near zero
orthogonal should be near zero = 2.61041188665e-14
 
a1*v = lambda*v difference should be near zero
len(ve)= 4
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
 
trace = sum ? 1.04166666667 1.04166666667
 
max sum row col > max abs eigenvalue? 1.28333333333 0.977556281151
 
 
test complex eigenvalues on diagonal
a2=
[[ 0.+0.j  0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  1.+1.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  2.+2.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j  3.+3.j]]
lambda=
[ 0.+0.j  1.+1.j  2.+2.j  3.+3.j]
vectors=
[[ 1.+0.j  0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  1.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  1.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j  1.+0.j]]
 
det|a - lambda*I| should be near zero
check eig =  0j , det =  2.36205593348e-09
check eig =  (1+1j) , det =  2.36205593348e-09
check eig =  (2+2j) , det =  2.36205593348e-09
check eig =  (3+3j) , det =  2.36205593348e-09
 
sum of abs of dot product of all v should be near zero
orthogonal should be near zero = 0.0
 
a1*v = lambda*v difference should be near zero
len(ve)= 4
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 1 0 0]
va= [0 0 0 0]
ve=  [0 0 2 0]
va= [0 0 0 3]
ve=  [0 0 0 3]
 
trace = sum ? (6+6j) (6+6j)
 
max sum row col > max abs eigenvalue? 4.24264068712 4.24264068712
 
 
generate random matrix, find and test eigenvalues
a3=
[[ 0.05694755  0.80135883  0.1878449   0.04188963]
 [ 0.67674808  0.67773654  0.367826    0.56855318]
 [ 0.68535587  0.53457797  0.03402587  0.19757729]
 [ 0.34421867  0.29501979  0.43387846  0.6237352 ]]
lambda=
[ 1.70744075 -0.433552   -0.02306597  0.14162236]
vectors=
[[ 0.38448597  0.62496189  0.23459936 -0.34966034]
 [ 0.66709117 -0.21912589 -0.17509716  0.06045826]
 [ 0.42659903 -0.73237473  0.77266199 -0.57919652]
 [ 0.47452417  0.15822053 -0.56329173  0.73390315]]
 
det|a - lambda*I| should be near zero
check eig =  1.70744075126 , det =  2.36205593348e-09
check eig =  -0.433551998058 , det =  2.36205593348e-09
check eig =  -0.0230659675991 , det =  2.36205593348e-09
check eig =  0.141622361626 , det =  2.36205593348e-09
 
sum of abs of dot product of all v should be near zero
orthogonal should be near zero = 1.72825240433
 
a1*v = lambda*v difference should be near zero
len(ve)= 4
va= [0 0 0 0]
ve=  [0 1 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
va= [0 0 0 0]
ve=  [0 0 0 0]
 
trace = sum ? 1.39244514723 1.39244514723
 
max sum row col > max abs eigenvalue? 2.30869312694 1.70744075126