Я получил разные матрицы после применения logm к унитарной матрице (H = i * logm (U)) из 2020 IBM-challenge 4 с использованием MATLAB и scipy.linalg. И я почти уверен, что результат MATLAB верен, потому что, если U - унитарная матрица, H (где H = iln (U)) должна быть эрмитовой матрицей. Но scipy результат не дает эрмитовой матрицы.
(я пробовал использовать scipy 1.4.0, 1.4.1, 1.5.0 и 1.5.1 и получил ту же проблему)
# ibm challenge
U = np.array([[-0.21338835+0.33838835j, -0.14016504-0.08838835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.08838835-0.03661165j, -0.08838835-0.21338835j],
[-0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.08838835-0.21338835j, 0.08838835-0.03661165j],
[ 0.21338835-0.08838835j, 0.03661165+0.08838835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.16161165+0.03661165j, 0.08838835-0.39016504j],
[ 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.08838835-0.39016504j, 0.16161165+0.03661165j],
[ 0.08838835-0.03661165j, -0.08838835-0.21338835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.39016504+0.08838835j, -0.03661165+0.16161165j],
[-0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.03661165+0.16161165j, 0.39016504+0.08838835j],
[-0.08838835+0.14016504j, 0.33838835+0.21338835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.21338835-0.08838835j, 0.03661165+0.08838835j],
[ 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j],
[ 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j],
[ 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.33838835+0.21338835j, -0.08838835+0.14016504j],
[ 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j],
[-0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.08838835-0.21338835j, 0.08838835-0.03661165j],
[ 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j],
[ 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.14016504-0.08838835j, -0.21338835+0.33838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j],
[ 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.16161165+0.03661165j, 0.08838835-0.39016504j, 0.39016504+0.08838835j, -0.03661165+0.16161165j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, -0.08838835+0.14016504j, 0.33838835+0.21338835j, 0.08838835-0.03661165j, -0.08838835-0.21338835j, 0.21338835-0.08838835j, 0.03661165+0.08838835j, -0.21338835+0.33838835j, -0.14016504-0.08838835j],
[-0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.08838835-0.39016504j, 0.16161165+0.03661165j, -0.03661165+0.16161165j, 0.39016504+0.08838835j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, 0.33838835+0.21338835j, -0.08838835+0.14016504j, -0.08838835-0.21338835j, 0.08838835-0.03661165j, 0.03661165+0.08838835j, 0.21338835-0.08838835j, -0.14016504-0.08838835j, -0.21338835+0.33838835j]])
#scipy
H = 1j*scipy.linalg.logm(U)
np.around(H,decimals=8)
#output from scipy
array([[-1.17809725+0.j , 0.38099484+0.00946823j,
0.43661075-0.01263701j, -0.03220742+0.00316877j,
0.03220742-0.00316877j, -0.04391167+0.012637j ,
-0.77369392-0.00946824j, 0. -0.j ,
0.36049166+0.00316876j, 0.04391166-0.012637j ,
-0.01170425+0.00946824j, -0.78539816-0.j ,
0.78539816+0.j , 0.79710241-0.00946824j,
-0.04391167+0.012637j , 0.03220742-0.00316877j],
[ 0.39269909-0.j , -1.06525495+0.06921355j,
-0.23366775-0.32686554j, 0.51352453+0.257652j ,
-0.12082544-0.257652j , 0.23366774+0.32686554j,
-0.1128423 -0.06921354j, -0.78539816+0.j ,
0.12082544+0.257652j , 0.15903134-0.32686555j,
-0.67255586+0.06921354j, -0. +0.j ,
0.78539816-0.j , 0.67255586-0.06921354j,
0.23366774+0.32686554j, -0.12082544-0.257652j ],
[ 0.39269909-0.j , -0.28325293+0.10409559j,
-0.26318476+0.04375582j, -0.23896048-0.14785141j,
-0.1537386 +0.14785141j, -0.91491249-0.04375582j,
0.28325293-0.10409559j, 0. -0.j ,
-0.63165957-0.1478514j , 0.12951433+0.04375582j,
0.10944616+0.10409558j, -0. +0.j ,
0. +0.j , 0.28325293-0.10409559j,
-0.12951433-0.04375582j, 1.41705772+0.14785141j],
[-0. +0.j , 0.57481396-0.18277737j,
-0.33245733+0.29574672j, -0.63505571-0.11296936j,
-0.54304154+0.11296936j, -0.06024175-0.29574673j,
-0.18211488+0.18277737j, 0. +0.j ,
-0.24235662-0.11296936j, -0.72515642+0.29574673j,
0.18211487-0.18277736j, 0.39269909-0.j ,
0. -0.j , -0.18211488+0.18277737j,
1.51055458-0.29574673j, 0.24235663+0.11296936j],
[-0. +0.j , -0.18211488+0.18277737j,
-0.06024175-0.29574673j, -0.54304154+0.11296936j,
-0.63505571-0.11296936j, -0.33245733+0.29574672j,
0.57481396-0.18277737j, -0. +0.j ,
0.24235663+0.11296936j, 1.51055458-0.29574673j,
-0.18211488+0.18277737j, 0. -0.j ,
0.39269909-0.j , 0.18211487-0.18277736j,
-0.72515642+0.29574673j, -0.24235662-0.11296936j],
[ 0. +0.j , 0.28325293-0.10409559j,
-0.91491249-0.04375582j, -0.1537386 +0.14785141j,
-0.23896048-0.14785141j, -0.26318476+0.04375582j,
-0.28325293+0.10409559j, 0.39269909-0.j ,
1.41705772+0.14785141j, -0.12951433-0.04375582j,
0.28325293-0.10409559j, 0. -0.j ,
-0. +0.j , 0.10944616+0.10409558j,
0.12951433+0.04375582j, -0.63165957-0.1478514j ],
[-0.78539816-0.j , -0.1128423 -0.06921354j,
0.23366774+0.32686554j, -0.12082544-0.257652j ,
0.51352453+0.257652j , -0.23366775-0.32686554j,
-1.06525495+0.06921355j, 0.39269909-0.j ,
-0.12082544-0.257652j , 0.23366774+0.32686554j,
0.67255586-0.06921354j, 0.78539816+0.j ,
-0. +0.j , -0.67255586+0.06921354j,
0.15903134-0.32686555j, 0.12082544+0.257652j ],
[ 0. +0.j , -0.77369392-0.00946824j,
-0.04391167+0.012637j , 0.03220742-0.00316877j,
-0.03220742+0.00316877j, 0.43661075-0.01263701j,
0.38099484+0.00946823j, -1.17809725+0.j ,
0.03220742-0.00316877j, -0.04391167+0.012637j ,
0.79710241-0.00946824j, 0.78539816+0.j ,
-0.78539816-0.j , -0.01170425+0.00946824j,
0.04391166-0.012637j , 0.36049166+0.00316876j],
[ 0.39269909-0.j , 0.18211487-0.18277736j,
-0.72515642+0.29574673j, -0.24235662-0.11296936j,
0.24235663+0.11296936j, 1.51055458-0.29574673j,
-0.18211488+0.18277737j, -0. -0.j ,
-0.63505571-0.11296936j, -0.33245733+0.29574672j,
0.57481396-0.18277737j, -0. +0.j ,
-0. +0.j , -0.18211488+0.18277737j,
-0.06024175-0.29574673j, -0.54304154+0.11296936j],
[-0. +0.j , 0.10944616+0.10409558j,
0.12951433+0.04375582j, -0.63165957-0.1478514j ,
1.41705772+0.14785141j, -0.12951433-0.04375582j,
0.28325293-0.10409559j, -0. +0.j ,
-0.23896048-0.14785141j, -0.26318476+0.04375582j,
-0.28325293+0.10409559j, 0.39269909-0.j ,
0. +0.j , 0.28325293-0.10409559j,
-0.91491249-0.04375582j, -0.1537386 +0.14785141j],
[-0. +0.j , -0.67255586+0.06921354j,
0.15903134-0.32686555j, 0.12082544+0.257652j ,
-0.12082544-0.257652j , 0.23366774+0.32686554j,
0.67255586-0.06921354j, 0.78539816-0.j ,
0.51352453+0.257652j , -0.23366775-0.32686554j,
-1.06525495+0.06921355j, 0.39269909-0.j ,
-0.78539816-0.j , -0.1128423 -0.06921354j,
0.23366774+0.32686554j, -0.12082544-0.257652j ],
[-0.78539816-0.j , -0.01170425+0.00946824j,
0.04391166-0.012637j , 0.36049166+0.00316876j,
0.03220742-0.00316877j, -0.04391167+0.012637j ,
0.79710241-0.00946824j, 0.78539816-0.j ,
-0.03220742+0.00316877j, 0.43661075-0.01263701j,
0.38099484+0.00946823j, -1.17809725+0.j ,
0. +0.j , -0.77369392-0.00946824j,
-0.04391167+0.012637j , 0.03220742-0.00316877j],
[ 0.78539816-0.j , 0.79710241-0.00946824j,
-0.04391167+0.012637j , 0.03220742-0.00316877j,
0.36049166+0.00316876j, 0.04391166-0.012637j ,
-0.01170425+0.00946824j, -0.78539816-0.j ,
0.03220742-0.00316877j, -0.04391167+0.012637j ,
-0.77369392-0.00946824j, -0. -0.j ,
-1.17809725+0.j , 0.38099484+0.00946823j,
0.43661075-0.01263701j, -0.03220742+0.00316877j],
[ 0.78539816+0.j , 0.67255586-0.06921354j,
0.23366774+0.32686554j, -0.12082544-0.257652j ,
0.12082544+0.257652j , 0.15903134-0.32686555j,
-0.67255586+0.06921354j, -0. +0.j ,
-0.12082544-0.257652j , 0.23366774+0.32686554j,
-0.1128423 -0.06921354j, -0.78539816-0.j ,
0.39269909-0.j , -1.06525495+0.06921355j,
-0.23366775-0.32686554j, 0.51352453+0.257652j ],
[-0. -0.j , 0.28325293-0.10409559j,
-0.12951433-0.04375582j, 1.41705772+0.14785141j,
-0.63165957-0.1478514j , 0.12951433+0.04375582j,
0.10944616+0.10409558j, -0. +0.j ,
-0.1537386 +0.14785141j, -0.91491249-0.04375582j,
0.28325293-0.10409559j, 0. +0.j ,
0.39269909-0.j , -0.28325293+0.10409559j,
-0.26318476+0.04375582j, -0.23896048-0.14785141j],
[-0. +0.j , -0.18211488+0.18277737j,
1.51055458-0.29574673j, 0.24235663+0.11296936j,
-0.24235662-0.11296936j, -0.72515642+0.29574673j,
0.18211487-0.18277736j, 0.39269909-0.j ,
-0.54304154+0.11296936j, -0.06024175-0.29574673j,
-0.18211488+0.18277737j, -0. +0.j ,
-0. +0.j , 0.57481396-0.18277737j,
-0.33245733+0.29574672j, -0.63505571-0.11296936j]])
#MATLAB input
U = [-0.21338835+0.33838835i -0.14016504-0.08838835i 0.21338835-0.08838835i 0.03661165+0.08838835i 0.08838835-0.03661165i -0.08838835-0.21338835i -0.08838835+0.14016504i 0.33838835+0.21338835i 0.21338835-0.08838835i 0.03661165+0.08838835i 0.39016504+0.08838835i -0.03661165+0.16161165i 0.16161165+0.03661165i 0.08838835-0.39016504i 0.08838835-0.03661165i -0.08838835-0.21338835i;
-0.14016504-0.08838835i -0.21338835+0.33838835i 0.03661165+0.08838835i 0.21338835-0.08838835i -0.08838835-0.21338835i 0.08838835-0.03661165i 0.33838835+0.21338835i -0.08838835+0.14016504i 0.03661165+0.08838835i 0.21338835-0.08838835i -0.03661165+0.16161165i 0.39016504+0.08838835i 0.08838835-0.39016504i 0.16161165+0.03661165i -0.08838835-0.21338835i 0.08838835-0.03661165i;
0.21338835-0.08838835i 0.03661165+0.08838835i -0.21338835+0.33838835i -0.14016504-0.08838835i -0.08838835+0.14016504i 0.33838835+0.21338835i 0.08838835-0.03661165i -0.08838835-0.21338835i 0.39016504+0.08838835i -0.03661165+0.16161165i 0.21338835-0.08838835i 0.03661165+0.08838835i 0.08838835-0.03661165i -0.08838835-0.21338835i 0.16161165+0.03661165i 0.08838835-0.39016504i]
H = i*logm(U)
#output from MATLAB
H =
Columns 1 through 5
-0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i 0.3927 + 0.0000i
0.0000 - 0.0000i -0.0000 + 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i 0.3927 - 0.0000i
0.0000 - 0.0000i -0.3927 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i -0.3927 - 0.0000i
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0.3927 - 0.0000i 0.3927 - 0.0000i -0.3927 - 0.0000i -1.1781 + 0.0000i -0.0000 + 0.0000i
0.3927 - 0.0000i 0.3927 - 0.0000i -1.1781 + 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i
-0.3927 - 0.0000i -1.1781 - 0.0000i 0.3927 + 0.0000i 0.3927 + 0.0000i 0.0000 - 0.0000i
-1.1781 + 0.0000i -0.3927 - 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i -0.3927 + 0.0000i
0.0000 - 0.0000i -0.3927 + 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i -0.3927 - 0.0000i
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0.3927 - 0.0000i -0.3927 + 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i 0.3927 + 0.0000i
-0.3927 + 0.0000i 1.1781 - 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i 0.0000 - 0.0000i
1.1781 - 0.0000i -0.3927 - 0.0000i 0.3927 - 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i
0.3927 - 0.0000i 0.3927 + 0.0000i -0.3927 + 0.0000i 1.1781 - 0.0000i -0.3927 + 0.0000i
0.3927 - 0.0000i 0.3927 + 0.0000i 1.1781 - 0.0000i -0.3927 - 0.0000i 0.3927 - 0.0000i
Columns 6 through 10
0.3927 + 0.0000i -0.3927 + 0.0000i -1.1781 - 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i
0.3927 - 0.0000i -1.1781 + 0.0000i -0.3927 - 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i
-1.1781 - 0.0000i 0.3927 - 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i
-0.3927 + 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i
0.0000 - 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i -0.3927 + 0.0000i 1.1781 - 0.0000i
-0.0000 + 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i 1.1781 - 0.0000i -0.3927 - 0.0000i
-0.3927 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i 0.3927 + 0.0000i 0.3927 + 0.0000i
0.0000 - 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i 0.3927 - 0.0000i 0.3927 - 0.0000i
1.1781 - 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i
-0.3927 - 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i
0.3927 - 0.0000i -0.3927 - 0.0000i 1.1781 + 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i
0.3927 + 0.0000i 1.1781 + 0.0000i -0.3927 - 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i
-0.3927 + 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i
0.0000 - 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i 0.3927 - 0.0000i
0.3927 - 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i -0.3927 - 0.0000i -1.1781 - 0.0000i
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Columns 11 through 15
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0.3927 - 0.0000i -0.3927 + 0.0000i 1.1781 - 0.0000i -0.3927 - 0.0000i 0.3927 - 0.0000i
0.0000 - 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i 0.3927 + 0.0000i -0.3927 + 0.0000i
-0.3927 + 0.0000i 0.0000 - 0.0000i 0.3927 + 0.0000i 0.3927 - 0.0000i 1.1781 + 0.0000i
0.3927 + 0.0000i 0.3927 + 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i -0.3927 + 0.0000i
0.3927 + 0.0000i 0.3927 + 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i 0.3927 - 0.0000i
-0.3927 - 0.0000i 1.1781 - 0.0000i -0.3927 + 0.0000i 0.3927 - 0.0000i 0.0000 - 0.0000i
1.1781 + 0.0000i -0.3927 - 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i -0.3927 + 0.0000i
0.0000 - 0.0000i -0.3927 + 0.0000i 0.3927 + 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i
-0.3927 + 0.0000i 0.0000 - 0.0000i 0.3927 + 0.0000i 0.3927 - 0.0000i -1.1781 - 0.0000i
-0.0000 + 0.0000i 0.0000 - 0.0000i -0.3927 + 0.0000i -1.1781 - 0.0000i 0.3927 - 0.0000i
0.0000 - 0.0000i -0.0000 + 0.0000i -1.1781 - 0.0000i -0.3927 + 0.0000i 0.3927 + 0.0000i
-0.3927 + 0.0000i -1.1781 - 0.0000i -0.0000 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i
-1.1781 - 0.0000i -0.3927 - 0.0000i 0.0000 - 0.0000i -0.0000 + 0.0000i -0.3927 + 0.0000i
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0.3927 - 0.0000i 0.3927 - 0.0000i -0.3927 + 0.0000i 0.0000 - 0.0000i 0.0000 - 0.0000i
Column 16
0.3927 - 0.0000i
0.3927 + 0.0000i
1.1781 - 0.0000i
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0.3927 - 0.0000i
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0.0000 - 0.0000i
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0.3927 - 0.0000i
0.3927 + 0.0000i
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0.0000 - 0.0000i
0.0000 - 0.0000i
-0.0000 + 0.0000i
#output from MATLAB in numpy array
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