title: numpy eigenvalues correct but eigenvectors wrong
body: <p>My code is </p>
  
  <pre><code>print numpy.linalg.eig([[1, 2, 3], [5, 4, 9], [63, 7, 5]])
  </code></pre>
  
  <p>The output is </p>
  
  <p>(array([ 21.61455381,  -9.76720959,  -1.84734422]), array([[-0.17186028, -0.14352001,  0.03651047],
     [-0.48646994, -0.50447076, -0.8471429 ],
     [-0.85662772,  0.8514172 ,  0.53010931]]))</p>
  
  <p>I am using an online eigenvector calcualtor to verify <a href="http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert2.htm" rel="nofollow">http://www.arndt-bruenner.de/mathe/scripts/engl_eigenwert2.htm</a>
  which gives the following answer:</p>
  
  <p>Real Eigenvalues:   { -9.767209588804548 ;  -1.8473442163236111 ;  21.61455380512816 }</p>
  
  <p>Eigenvectors:</p>
  
  <p>for Eigenvalue -9.767209588804548:
     [ -0.1685660264358372 ; -0.5925071319066865 ; 1 ]</p>
  
  <p>for Eigenvalue -1.8473442163236111:
     [ 0.06887346700751434 ; -1.5980532339710003 ; 1 ]</p>
  
  <p>for Eigenvalue 21.61455380512816:
     [ 0.20062423644695662 ; 0.5678895584242702 ; 1 ]</p>
  
  <p>The values obviously don't match. Where am I going wrong?</p>