title: Matrix to quaternion and back does not give same result
body: <p>I'm converting a matrix (M) to a quaternion so that I can e.g. lerp between two different transformation matrices making a smooth animation of an image where I need to make the video frames myself.</p>
  
  <p>When I convert back from the quaternion to a matrix as a test, this new matrix is very far from being the same as the one that became the quat.</p>
  
  <pre><code>import numpy as np
  from transforms3d import quaternions
  
  M = np.array([[  0.757403109,  -0.186744161,   145.541734],
   [ -0.154492906,   0.626185286,   100.878814],
   [ -0.000294826495,  -0.000344726091,   1.00000000]])
  
  
  quat = quaternions.mat2quat(M)
  
  
  testM = quaternions.quat2mat(quat)
  print("TEST: M original")
  print(M)
  print("TEST: quat back to mat (testM)")
  print(testM)
  print("Why not the same")
  print ("quat")
  print(quat)
  print("quat of testM")
  print(quaternions.mat2quat(testM))
  
  #Scaling gives same result, scale M to be -1. to 1
  mmax = np.amax(M)
  scaleTestM = M / mmax
  print("M Scaled")
  print(scaleTestM)
  quatOfScaled = quaternions.mat2quat(scaleTestM)
  print("Quat of scaled")
  print(quaternions.quat2mat(quatOfScaled))
  </code></pre>
  
  <p>Do I miss something of what a quaternion actually can represent or is the code wrong?
  If this cannot work, other suggestions on how to move smoothly between two transformation matrices is appreciated.</p>
  
  <p>Python 3.6</p>
  
  <p>Console output is this:</p>
  
  <blockquote>
  <pre><code>    TEST: M original
     [[  7.57403109e-01  -1.86744161e-01   1.45541734e+02]
      [ -1.54492906e-01   6.26185286e-01   1.00878814e+02]
       [ -2.94826495e-04  -3.44726091e-04   1.00000000e+00]]
      TEST: quat back to mat (testM)
      [[ 0.38627453 -0.42005089  0.8211877 ]
       [-0.54462197  0.61466344  0.57059247]
       [-0.74443193 -0.6676422   0.00865989]]
      Why not the same
      quat
      [ 0.70880143 -0.43673539  0.55220671 -0.04393723]
      quat of testM
      [ 0.70880143 -0.43673539  0.55220671 -0.04393723]
      M Scaled
      [[  5.20402697e-03  -1.28309699e-03   1.00000000e+00]
       [ -1.06150244e-03   4.30244486e-03   6.93126372e-01]
       [ -2.02571789e-06  -2.36857210e-06   6.87088145e-03]]
      Quat of scaled
      [[ 0.38627453 -0.42005089  0.8211877 ]
       [-0.54462197  0.61466344  0.57059247]
       [-0.74443193 -0.6676422   0.00865989]]
  </code></pre>
  </blockquote>