Eigenvalues and Eigenvectors Python Example
In this post, you will learn about how to calculate Eigenvalues and Eigenvectors using Python code examples. Before getting ahead and learning the code examples, you may want to check out this post on when & why to use Eigenvalues and Eigenvectors. As a machine learning Engineer / Data Scientist, you must get a good understanding of Eigenvalues / Eigenvectors concepts as it proves to be very useful in feature extraction techniques such as principal components analysis. Python Numpy package is used for illustration purpose. The following topics are covered in this post:
In this section, you will learn about how to create Eigenvalues and Eigenvectors for a given square matrix (transformation matrix) using Python Numpy library. Here are the steps:
import numpy as np
from sklearn.preprocessing import StandardScaler
from numpy.linalg import eig
#
# Percentage of marks and no. of hours studied
#
students = np.array([[85.4, 5],
[82.3, 6],
[97, 7],
[96.5, 6.5]])
#
# Scale the features
#
sc = StandardScaler()
students_scaled = sc.fit_transform(students)
#
# Calculate covariance matrix; One can also use the following
# code: np.cov(students_scaled, rowvar=False)
#
cov_matrix = np.cov(students_scaled.T)
#
# Calculate Eigenvalues and Eigenmatrix
#
eigenvalues, eigenvectors = eig(cov_matrix)
Here is how the output of above looks like:
Let’s confirm whether the above is correct by calculating LHS and RHS of the following and making sure that LHS = RHS. A represents the transformation matrix (cob_matrix in above example), x represents eigenvectors and [latex]\lambda[/latex] represents eigenvalues
[latex]
Ax = \lambda x
[/latex]
Here is the code comparing LHS to RHS
#
# LHS
#
cov_matrix.dot(eigenvectors[:, 0])
#
# RHS
#
eigenvalues[0]*eigenvectors[:, 0]
From the output represented in the picture below, it does confirm that above calculation done by Numpy linalg.eig method is correct.
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VERY USEFUL
Thank you