title: Python eigenvalues and eigenvectors
body: <p>I have a 336x336 coinsurance matrix and I calculated the eigenvalues and eigenvectors using numpy as follows with sorting.</p>
  
  <pre><code>evals, evecs = np.linalg.eig(cov)
  idx = evals.argsort()   
  evals = evals[idx] 
  evecs = evecs[:,idx]
  </code></pre>
  
  <p>The problem is that the last value in evals is strange compared to other values.
  Something like this:</p>
  
  <pre><code>    evals[:3]
      [ -6.11117191e-19  -6.11117191e-19  -1.08420217e-19]
      evals[-3:]
      [  4.29345466e-19   7.08196415e-19   1.69419875e-02]
  </code></pre>
  
  <p>The highest eigenvalue, 1.69419875e-02, is very high compared to other values. I have checked all the 336 eigenvalues and all except this one is more or less in same range.</p>
  
  <p>Can anyone tell me why is this so.</p>
  
  <p>Hi mrcl,
     Thank you for your reply. I have generated the 8x8 covariance matrix using precision suggested by you. It now looks like this:</p>
  
  <pre><code>[[  0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00]
    [  0.00e+00   4.62e-05   9.25e-05   4.62e-05   0.00e+00  -9.25e-05  -4.62e-05  -4.62e-05]
    [  0.00e+00   9.25e-05   1.85e-04   9.25e-05   0.00e+00  -1.85e-04  -9.25e-05  -9.25e-05]
    [  0.00e+00   4.62e-05   9.25e-05   4.62e-05   0.00e+00  -9.25e-05  -4.62e-05  -4.62e-05]
    [  0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00   0.00e+00]
    [  0.00e+00  -9.25e-05  -1.85e-04  -9.25e-05   0.00e+00   1.85e-04   9.25e-05   9.25e-05]
    [  0.00e+00  -4.62e-05  -9.25e-05  -4.62e-05   0.00e+00   9.25e-05   4.62e-05   4.62e-05]
    [  0.00e+00  -4.62e-05  -9.25e-05  -4.62e-05   0.00e+00   9.25e-05   4.62e-05   4.62e-05]]
  </code></pre>
  
  <p>For column 1 and row 1, I am not sure why all is zero, I calculated manually also the covariance of these column and row and it is zero only, may be there is not much change in the original values, The original values are:</p>
  
  <pre><code>0.06  0.05  0.05  0.08  0.05  0.06  0.06  0.02
  
  0.06  0.04  0.03  0.07  0.05  0.08  0.07  0.03
  </code></pre>
  
  <p>Thanks!</p>