

In [1]:

    
import numpy as np
import numpy.linalg as linalg

Linear Algebra with NumPy

With Numpy it's also easy to generate matrices and perform operations on them.



In [2]:

    
A = np.matrix([[1,2], [3,4]])
A









    Out[2]:





matrix([[1, 2],
        [3, 4]])



In [3]:

    
A_inv = linalg.inv(A)
A_inv









    Out[3]:





matrix([[-2. ,  1. ],
        [ 1.5, -0.5]])



In [4]:

    
A * A_inv









    Out[4]:





matrix([[  1.00000000e+00,   0.00000000e+00],
        [  8.88178420e-16,   1.00000000e+00]])

Linalg

The linalg library provides a number of useful linear algebra routines.



In [5]:

    
eigenvalues, eigenvectors = linalg.eig(A)
eigenvalues









    Out[5]:





array([-0.37228132,  5.37228132])



In [6]:

    
eigenvectors









    Out[6]:





matrix([[-0.82456484, -0.41597356],
        [ 0.56576746, -0.90937671]])

$3 \times x_0 + x_1 = 9$

$x_0 + 2 \times x_1 = 8$



In [7]:

    
a = np.array([[3, 1], [1,2]])
b = np.array([9,8])
np.linalg.solve(a,b)









    Out[7]:





array([ 2.,  3.])