Book Image

Python Data Analysis - Second Edition

By : Ivan Idris
Book Image

Python Data Analysis - Second Edition

By: Ivan Idris

Overview of this book

Data analysis techniques generate useful insights from small and large volumes of data. Python, with its strong set of libraries, has become a popular platform to conduct various data analysis and predictive modeling tasks. With this book, you will learn how to process and manipulate data with Python for complex analysis and modeling. We learn data manipulations such as aggregating, concatenating, appending, cleaning, and handling missing values, with NumPy and Pandas. The book covers how to store and retrieve data from various data sources such as SQL and NoSQL, CSV fies, and HDF5. We learn how to visualize data using visualization libraries, along with advanced topics such as signal processing, time series, textual data analysis, machine learning, and social media analysis. The book covers a plethora of Python modules, such as matplotlib, statsmodels, scikit-learn, and NLTK. It also covers using Python with external environments such as R, Fortran, C/C++, and Boost libraries.
Table of Contents (22 chapters)
Python Data Analysis - Second Edition
Credits
About the Author
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
Key Concepts
Online Resources

Finding eigenvalues and eigenvectors with NumPy


The eigenvalues are scalar solutions to the equation Ax = ax, where A is a two-dimensional matrix and x is a one-dimensional vector. The eigenvectors are vectors corresponding to eigenvalues.

Note

The eigenvalues and eigenvectors are fundamental in mathematics, and are used in many important algorithms, such as principal component analysis (PCA). PCA can be used to simplify the analysis of large datasets.

The eigvals() subroutine in the numpy.linalg package computes eigenvalues. The eig() function gives back a tuple holding eigenvalues and eigenvectors.

We will obtain the eigenvalues and eigenvectors of a matrix with the eigvals() and eig() functions of the numpy.linalg subpackage. We will check the outcome by applying the dot() function:

import numpy as np 
 
A = np.mat("3 -2;1 0") 
print("A\n", A) 
 
print("Eigenvalues", np.linalg.eigvals(A)) 
 
eigenvalues, eigenvectors = np.linalg.eig(A) 
print("First...