title: Strange behaviour of numpy eigenvector: bug or no bug
body: <p>NumPy's eigenvector solution differs from Wolfram Alpha and my personal calculation by hand.</p>
  
  <pre class="lang-py prettyprint-override"><code>&gt;&gt;&gt; import numpy.linalg
  &gt;&gt;&gt; import numpy as np
  &gt;&gt;&gt; numpy.linalg.eig(np.array([[-2, 1], [2, -1]]))
  (array([-3.,  0.]), array([[-0.70710678, -0.4472136 ],
         [ 0.70710678, -0.89442719]]))
  </code></pre>
  
  <p>Wolfram Alpha <a href="https://www.wolframalpha.com/input/?i=eigenvectors+%7B%7B-2,1%7D,%7B%2B2,-1%7D%7D" rel="nofollow noreferrer">https://www.wolframalpha.com/input/?i=eigenvectors+%7B%7B-2,1%7D,%7B%2B2,-1%7D%7D</a> and my personal calculation give the eigenvectors (-1, 1) and (2, 1). The NumPy solution however differs.</p>
  
  <p>NumPy's calculated eigenvalues however are confirmed by Wolfram Alpha and my personal calculation.</p>
  
  <p>So, is this a bug in NumPy or is my understanding of math to simple? A similar thread <a href="https://stackoverflow.com/questions/26589448/numpy-seems-to-produce-incorrect-eigenvectors">Numpy seems to produce incorrect eigenvectors</a> sees the main difference in rounding/scaling of the eigenvectors but the deviation between the solutions would be massive.</p>
  
  <p>Regards</p>