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The reason is P is not symmetric!!!!!!!!!!!!!!
P-P.T
array([[ 0. , 0. , 0.3924 , 0.7848 , 1.15153704,
1.46694816, 1.70704875, 1.85121094, 1.88373214, 1.79518415],
[ 0. , 0. , 0. , 0.3924 , 0.7848 ,
1.15153704, 1.46694816, 1.70704876, 1.85121095, 1.88373214],
[-0.3924 , 0. , 0. , 0. , 0.3924 ,
0.7848 , 1.15153704, 1.46694816, 1.70704876, 1.85121095],
[-0.7848 , -0.3924 , 0. , 0. , 0. ,
0.3924 , 0.7848 , 1.15153704, 1.46694816, 1.70704876],
[-1.15153704, -0.7848 , -0.3924 , 0. , 0. ,
0. , 0.3924 , 0.7848 , 1.15153704, 1.46694816],
[-1.46694816, -1.15153704, -0.7848 , -0.3924 , 0. ,
0. , 0. , 0.3924 , 0.7848 , 1.15153704],
[-1.70704875, -1.46694816, -1.15153704, -0.7848 , -0.3924 ,
0. , 0. , 0. , 0.3924 , 0.7848 ],
[-1.85121094, -1.70704876, -1.46694816, -1.15153704, -0.7848 ,
-0.3924 , 0. , 0. , 0. , 0.3924 ],
[-1.88373214, -1.85121095, -1.70704876, -1.46694816, -1.15153704,
-0.7848 , -0.3924 , 0. , 0. , 0. ],
[-1.79518415, -1.88373214, -1.85121095, -1.70704876, -1.46694816,
-1.15153704, -0.7848 , -0.3924 , 0. , 0. ]]
But P+P.T is symmetric!!!
(P+P.T)-(P+P.T).T
array([[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])
Thank you