Machine Learning

A Gentle Introduction to Matrix Factorization for Machine Learning

Last Updated on August 9, 2019

Many complex matrix operations cannot be solved efficiently or with stability using the limited precision of computers.

Matrix decompositions are methods that reduce a matrix into constituent parts that make it easier to calculate more complex matrix operations. Matrix decomposition methods, also called matrix factorization methods, are a foundation of linear algebra in computers, even for basic operations such as solving systems of linear equations, calculating the inverse, and calculating the determinant of a matrix.

In this tutorial, you will discover matrix decompositions and how to calculate them in Python.

After completing this tutorial, you will know:

  • What a matrix decomposition is and why these types of operations are important.
  • How to calculate an LU andQR matrix decompositions in Python.
  • How to calculate a Cholesky matrix decomposition in Python.

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.

  • Update Mar/2018: Fixed small typo in the description of QR Decomposition.
  • Update Jul/2019: Fixed a small typo when describing positive definite matrices.
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