docs: def eigenvalue_sensitivity(T, k):
      """
      calculate the sensitivity matrix for eigenvalue k given transition matrix T.
      Parameters
      ----------
      T : numpy.ndarray shape = (n, n)
          Transition matrix
      k : int
          eigenvalue index for eigenvalues order descending
  
      Returns
      -------
      x : ndarray, shape=(n, n)
          Sensitivity matrix for entry index around transition matrix T. Reversibility is not assumed.
      """
  
      eValues, rightEigenvectors = numpy.linalg.eig(T)
      leftEigenvectors = numpy.linalg.inv(rightEigenvectors)
  
      perm = numpy.argsort(eValues)[::-1]
  
      rightEigenvectors = rightEigenvectors[:, perm]
      leftEigenvectors = leftEigenvectors[perm]
  
      sensitivity = numpy.outer(leftEigenvectors[k], rightEigenvectors[:, k])
  
      return sensitivity