In [1]:

import numpy as np

In [2]:

a = np.random.randn(3)
a

Out[2]:

array([ 0.4951792 , -1.03530404,  1.70427995])

Let's zero out \(a_2\):

In [3]:

G = np.zeros((3, 3))

c = a[0]/sqrt(a[0]**2 + a[1]**2)
s = a[1]/sqrt(a[0]**2 + a[1]**2)

G[:2,:2] = np.array([
        [c, s],
        [-s, c]
        ])
G

Out[3]:

array([[ 0.43147946, -0.90212276,  0.        ],
       [ 0.90212276,  0.43147946,  0.        ],
       [ 0.        ,  0.        ,  0.        ]])

Anything wrong with \(G\)?

(Edit this cell for solution.)

In [4]:

np.dot(G, a)

Out[4]:

array([ 1.14763099,  0.        ,  0.        ])

Observations?