Gentle Introduction to Eigenvalues and Eigenvectors for Machine Learning

Last Updated on August 9, 2019

Matrix decompositions are a useful tool for reducing a matrix to their constituent parts in order to simplify a range of more complex operations.

Perhaps the most used type of matrix decomposition is the eigendecomposition that decomposes a matrix into eigenvectors and eigenvalues. This decomposition also plays a role in methods used in machine learning, such as in the the Principal Component Analysis method or PCA.

In this tutorial, you will discover the eigendecomposition, eigenvectors, and eigenvalues in linear algebra.

After completing this tutorial, you will know:

• What an eigendecomposition is and the role of eigenvectors and eigenvalues.
• How to calculate an eigendecomposition in Python with NumPy.
• How to confirm a vector is an eigenvector and how to reconstruct a matrix from eigenvectors and eigenvalues.

Kick-start your project with my new book Linear Algebra for Machine Learning, including step-by-step tutorials and the Python source code files for all examples.

Let’s get started.