title: Numpy - Modal matrix and diagonal Eigenvalues
body: <p>I wrote a simple Linear Algebra code in Python Numpy to calculate the Diagonal of EigenValues by calculating $M^{-1}.A.M$ (M is the Modal Matrix) and it's working strange.</p>
  
  <p>Here's the Code :</p>
  
  <pre><code>import numpy as np
  
  array = np.arange(16)
  array = array.reshape(4, -1)
  print(array)
  
  [[ 0  1  2  3]
   [ 4  5  6  7]
   [ 8  9 10 11]
   [12 13 14 15]]
  
  eigenvalues, eigenvectors = np.linalg.eig(array)
  
  print eigenvalues
  [  3.24642492e+01  -2.46424920e+00   1.92979794e-15  -4.09576009e-16]
  
  print eigenvectors
  [[-0.11417645 -0.7327781   0.54500164  0.00135151]
   [-0.3300046  -0.28974835 -0.68602671  0.40644504]
   [-0.54583275  0.15328139 -0.2629515  -0.8169446 ]
   [-0.76166089  0.59631113  0.40397657  0.40914805]]
  
  inverseEigenVectors = np.linalg.inv(eigenvectors) #M^(-1)
  diagonal= inverseEigenVectors.dot(array).dot(eigenvectors) #M^(-1).A.M
  
  print(diagonal)
  [[  3.24642492e+01  -1.06581410e-14   5.32907052e-15   0.00000000e+00]
   [  7.54951657e-15  -2.46424920e+00  -1.72084569e-15  -2.22044605e-16]
   [ -2.80737213e-15   1.46768503e-15   2.33547852e-16   7.25592561e-16]
   [ -6.22319863e-15  -9.69656080e-16  -1.38050658e-30   1.97215226e-31]]
  </code></pre>
  
  <p>the final 'diagonal' matrix should be a diagonal matrix with EigenValues on the main diagonal and zeros elsewhere. but it's not... the two first main diagonal values ARE eigenvalues but the two second aren't (although just like the two second eigenvalues, they are nearly zero).</p>
  
  <p>and by the way a number like $-1.06581410e-14$ is literally zero so how can I make numpy show them as zero?</p>
  
  <p>What am I doing wrong?</p>
  
  <p>Thanks...</p>