In order to calculate the Jordan form of a matrix, we will using the jordan_form function available within the sympy package. 

In the following code, we will look into obtaining the Jordan form of a given matrix in Python.

1. Import the relevant packages:

import numpy as np
from sympy import Matrix 

2. Initialize an array of numbers:

a = np.array([[5, 4, 2, 1], [0, 1, -1, -1], [-1, -1, 3, 0], [1, 1, -1, 2]]) 

3. Convert the array into a matrix format to be used by the jordan_form function:

m = Matrix(a) 

4. Apply the function on the preceding matrix:

P, J = m.jordan_form() 

5. Extract the output of the jordan_form, which is J:

J
Matrix([[1.0,   0,   0,   0],[  0, 2.0,   0,   0],[  0,   0, 4.0,   1],[  0,   0,   0, 4.0]])