Eigenvectors and eigenvalues with numpy

 

In machine learning, eigenvectors and eigenvalues come up quite a bit.

They are used in a variety of data science techniques such as Principal Component Analysis for dimensionality reduction of features.

Let’s take a look at how to calculate these linear algebra values efficiently with Numpy, a popular python numerical computation library, for a matrix.

Let’s first import our numpy package as np.

import numpy as np

Next, let’s create a sample matrix to calculate eigenvalues and eigenvectors for.

example_matrix = np.array([
  [1,2,3,4],
  [5,6,7,8],
  [9,10,11,12],
  [13,14,15,16]
])

Sweet, now we have a matrix to play with.

Numpy makes it super simple to get eigenvectors and eigenvalues for this.

eigenvalues, eigenvectors = np.linalg.eig(example_matrix)

Now, we can access the values of the eigenvalues and eigenvectors.

eigenvalues
# array([  3.62093727e+01,  -2.20937271e+00,  -4.65206927e-16, -2.13836670e-15])

eigenvectors
# array([[-0.15115432, -0.72704996,  0.02799736, -0.2749507 ],[-0.34923733, -0.28320876,  0.37038479,  0.71968426],[-0.54732033,  0.16063243, -0.82476165, -0.61451644],[-0.74540333,  0.60447363,  0.4263795 ,  0.16978287]])

The full code example can be found below.

import numpy as np

example_matrix = np.array([
  [1,2,3,4],
  [5,6,7,8],
  [9,10,11,12],
  [13,14,15,16]
])

eigenvalues, eigenvectors = np.linalg.eig(example_matrix)

eigenvalues
# array([  3.62093727e+01,  -2.20937271e+00,  -4.65206927e-16, -2.13836670e-15])

eigenvectors
# array([[-0.15115432, -0.72704996,  0.02799736, -0.2749507 ],[-0.34923733, -0.28320876,  0.37038479,  0.71968426],[-0.54732033,  0.16063243, -0.82476165, -0.61451644],[-0.74540333,  0.60447363,  0.4263795 ,  0.16978287]])