2150.sagews

v0=vector((1,0))
v1=vector((0,1))
m0=matrix([v0])
m1=matrix([v1])
p00 = m0.tensor_product(m0)
p01 = m0.tensor_product(m1)
p10 = m1.tensor_product(m0)
p11 = m1.tensor_product(m1)
psi00 = (p00 - p01 + p10 - p11)/2
psi01 = (p01 - p00 + p11 - p10)/2
psi10 = (p00 - p01 + p11 - p10)/2
psi11 = (p01 - p00 + p10 - p11)/2
s0 = (psi00.transpose()* psi00 + psi01.transpose()*psi01)/2
s1 = (psi10.transpose()* psi10 + psi11.transpose()*psi11)/2
(s0 - s1).eigenvalues()

[1, -1, 0, 0]

[0 0 1 0] [0 0 0 1] [1 0 0 0] [0 1 0 0]

[0 0|1 0] [0 0|0 0] [---+---] [0 0|0 0] [0 0|0 0]