Book Image

Python Data Analysis - Third Edition

By : Avinash Navlani, Ivan Idris
5 (1)
Book Image

Python Data Analysis - Third Edition

5 (1)
By: Avinash Navlani, Ivan Idris

Overview of this book

Data analysis enables you to generate value from small and big data by discovering new patterns and trends, and Python is one of the most popular tools for analyzing a wide variety of data. With this book, you’ll get up and running using Python for data analysis by exploring the different phases and methodologies used in data analysis and learning how to use modern libraries from the Python ecosystem to create efficient data pipelines. Starting with the essential statistical and data analysis fundamentals using Python, you’ll perform complex data analysis and modeling, data manipulation, data cleaning, and data visualization using easy-to-follow examples. You’ll then understand how to conduct time series analysis and signal processing using ARMA models. As you advance, you’ll get to grips with smart processing and data analytics using machine learning algorithms such as regression, classification, Principal Component Analysis (PCA), and clustering. In the concluding chapters, you’ll work on real-world examples to analyze textual and image data using natural language processing (NLP) and image analytics techniques, respectively. Finally, the book will demonstrate parallel computing using Dask. By the end of this data analysis book, you’ll be equipped with the skills you need to prepare data for analysis and create meaningful data visualizations for forecasting values from data.
Table of Contents (20 chapters)
Section 1: Foundation for Data Analysis
Section 2: Exploratory Data Analysis and Data Cleaning
Section 3: Deep Dive into Machine Learning
Section 4: NLP, Image Analytics, and Parallel Computing

Eigenvectors and Eigenvalues using NumPy

Eigenvectors and Eigenvalues are the tools required to understand linear mapping and transformation. Eigenvalues are solutions to the equation Ax = λx. Here, A is the square matrix, x is the eigenvector, and λ is eigenvalues. The numpy.linalg subpackage provides two functions, eig() and eigvals(). The eig() function returns a tuple of eigenvalues and eigenvectors, and eigvals() returns the eigenvalues.

Eigenvectors and eigenvalues are the core fundamentals of linear algebra. Eigenvectors and eigenvalues are used in SVD, spectral clustering, and PCA.

Let's compute the eigenvectors and eigenvalues of a matrix, as follows:

  • Create the matrix using the NumPy mat() function, like this:
# Import numpy
import numpy as np

# Create matrix using NumPy

This results in the following output:

Matrix: [[2 4]
[5 7]]
  • Compute eigenvectors and eigenvalues using the eig() function, like...