eigenvalues of a symmetric matrix returns empty set.

[Bharath M R]

Hi, 

   I was trying to implement rational chebychev series approximation to a function. This 

involves finding the eigen values of a symmetric matrix(for svd). I always get an empty set of

eigen values. 

Here is an example. The matrix is an symmetric matrix and hence it should have real eigen values.

```

from sympy import *

a = [[               40,  59.0372649711174,  91.9159715266083, -18.3586972981465, -26.5974423018762],

[ 59.0372649711174,  91.9159715266083,  149.966034521936, -26.5974423018762, -40.6785676729709],

[ 91.9159715266083,  149.966034521936,   254.33769719335, -40.6785676729709, -65.3185292247321],

[-18.3586972981465, -26.5974423018762, -40.6785676729709,  8.47893318890501,  12.0617341323178],

[-26.5974423018762, -40.6785676729709, -65.3185292247321,  12.0617341323178,  18.1185091129712]]

a = Matrix(a)

print a.eigenvals()

```

This return an empty eigen value set. Is this a bug? Is there any way around it?

Thanks,

Bharath M R

[Matthew Rocklin]

I'm not familiar with how the eigenvalue functions are written but I've used them on complex matrices and gotten results similar to yours. If your elements are numeric (as they appear to be in your example) then I would suggest doing this computation in numpy if that's possible. 

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[Bharath M R]

Thanks.

Doing it in numpy will add a numpy dependency for sympy. I think I should use the ``import_module``

and add the series expansion, which will only work if numpy is installled.

Thanks,

Bharath M R

[Matthew Rocklin]

Ah, I assume that this was for personal work and not for SymPy development. You could always improve the eigen-decomposition algorithm :)

Thanks,

Bharath M R

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