code: def rotate_vector(evecs, old_vector, rescale_factor, index):
      
      temp = 0
      for i in range(len(evecs)):
          temp += (evecs[i,index] * rescale_factor) * old_vector[i]
      return temp
docs: Function to find the position of the system(s) in one of the xi_i or mu_i
      directions.
  
      Parameters
      -----------
      evecs : numpy.matrix
          Matrix of the eigenvectors of the metric in lambda_i coordinates. Used
          to rotate to a Cartesian coordinate system.
      old_vector : list of floats or numpy.arrays
          The position of the system(s) in the original coordinates
      rescale_factor : float
          Scaling factor to apply to resulting position(s)
      index : int
          The index of the final coordinate system that is being computed. Ie.
          if we are going from mu_i -> xi_j, this will give j.
  
      Returns
      --------
      positions : float or numpy.array
          Position of the point(s) in the resulting coordinate.