There are there decompositions provided by numpy.linalg and in this section, we will cover two that are the most commonly used: singular value decomposition (svd) and QR factorization. Let's start by computing the eigenvalues and eigenvectors first. Before we get started, if you are not familiar with eigenvalues and eigenvectors, you may review them at https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors. Let's start:
In [41]: x = np.random.randint(0, 10, 9).reshape(3,3)
In [42]: x
Out[42]:
array([[ 1, 5, 0]
[ 7, 4, 0]
[ 2, 9, 8]])
In [42]: w, v = np.linalg.eig(x)
In [43]: w
Out[43]: array([ 8., 8.6033, -3.6033])
In [44]: v
Out[44]:
array([[ 0., 0.0384, 0.6834]
[ 0., 0.0583, -0.6292]
[ 1., 0.9976, 0.3702]]
)
In the previous example, first we created a 3 x 3 ndarray using numpy.random.randint
() and we computed the eigenvalues and eigenvectors...