I must be doing something wrong, trying to get eigenvectors
for a rather small hermitean 64x64 matrix 'm' (it is listed at the
end)
When I try to do
sage: m.eigenvalues()
sage departs into 'nirvana' and I have interupted the evaluation after
several minutes
When I do this in mathematica for the same matrix I get
Eigenvalues[m] // Timing
{1.5801, <-------------- !!
{1/2 (2 + Sqrt[13]), 1/2 (2 + Sqrt[5]), 1/2 (2 + Sqrt[5]),
1/2 (2 + Sqrt[5]), -(3/2), -(3/2), -(3/2), -(3/2), -(3/2), -(3/
2), -(3/2), 3/2, 1/4 (1 + Sqrt[17]), 1/4 (1 + Sqrt[17]),
1/4 (1 + Sqrt[17]), 1/4 (1 + Sqrt[17]), 1/4 (1 + Sqrt[17]),
1/4 (1 + Sqrt[17]), -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1,
1, 1, 1, 1/2 (2 - Sqrt[13]), 1/4 (1 - Sqrt[17]),
1/4 (1 - Sqrt[17]), 1/4 (1 - Sqrt[17]), 1/4 (1 - Sqrt[17]),
1/4 (1 - Sqrt[17]), 1/4 (1 - Sqrt[17]), -(1/2), -(1/2), -(1/2), 1/2,
1/2, 1/2, 1/2, 1/2, 1/2, 1/2, 1/2 (2 - Sqrt[5]), 1/2 (2 - Sqrt[5]),
1/2 (2 - Sqrt[5]), 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}
Any help? Thanks.
wb
I hope it is allowed with this group to post the matrix.
[[3/2,0,0,-1/2*I,0,0,-1/2*I,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,1/2,0,0,0,0,0,-1/2*I,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0],
[1/2*I,0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1/2,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0],
[1/2*I,
0,0,0,0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0],
[0,1/2*I,0,0,1/2*I,
0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,0,0,-1/2*I,
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,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,-1/2*I,
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,-1/2*I,
0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1/2*I,
0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0],
[1/2*I,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,
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,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0],
[0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0],
[0,0,1/2*I,0,0,0,0,0,1/2*I,
0,0,0,0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0],
[0,0,0,1/2*I,0,0,0,0,0,1/2*I,0,0,1/2*I,
0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,0,0,-1/2*I,
0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
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,-1/2,0,0,0,0,0,-1/2*I,
0,0,0,0,0,-1/2*I,
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,-1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
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,-1/2,0,0,-1/2*I,
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,-1/2*I,
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,-3/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,0,0,1/2*I,
0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,
0,0,-1/2*I,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,-1/2*I,
0,0,0,0,0,0],
[0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,-1/2*I,
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],
[0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0],
[0,0,0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,
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,-1/2*I,0,0],
[0,0,0,0,0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,1/2*I,0,0,0,0,0,1/2*I,
0,0,0,0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I],
[0,0,0,0,0,0,0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,1/2*I,0,0,0,0,0,1/2*I,
0,0,1/2*I,
0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,
0,0,-1/2*I,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0],
[1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,0,0,0,-1/2*I,
0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,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,-1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0],
[0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
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,-1/2,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,0,0,0],
[0,0,0,0,1/2*I,
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,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
0],
[0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,0,0,1/2*I,
0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1/2*I],
[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,-1/2,0,0,-1/2*I,
0,0,-1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,1/2*I,
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,-1/2,0,0,0,0,0,-1/2*I,
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,-3/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,-1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,1/2*I,0,0,0,0,0,-1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,0,0,0,0,0,1/2*I,
0,0,1/2*I,0,0,1/2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
[1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,-1/2*I,
0,0,-1/2*I,0,0,0,0,0,-1/2*I,0,0,0],
[0,1/2*I,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2*I,
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/2,0,0,0,0,0,-1/2*I,
0,0,0,0,0,-1/2*I,0,0],
[0,0,1/2*I,
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,-1/2,0,0,0,0,0,0,0,0,0,0,0,-1/2*I,
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