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Introduction

 
Mathematics is the core of all machine learning algorithms. And while it isn’t a prerequisite to have formal math education in order to become a data scientist, you need to understand the principles of the subject well enough to successfully build models that add value.

In an article I wrote previously, I explained the three branches of mathematics that were essential to gain a deeper understanding of ML algorithms — statistics, calculus, and linear algebra. 

This article will solely focus on linear algebra, as it forms the backbone of machine learning model implementation.

Linear algebra concepts like vectorization allow for faster computation speeds, and are implemented in libraries like Pandas, Scipy, and Scikit-Learn. 

Algorithms like PCA use matrix decomposition techniques to reduce the volume of a feature space.

The implementation of deep learning algorithms using libraries like Tensorflow requires a basic knowledge of linear algebra, as you will need to perform matrix manipulation and understand how tensors work.

Linear Algebra — Learning Resources

1. Immersive Linear Algebra  —  Textbook

This free textbook will take you through the basics of linear algebra. Here is the book’s table of contents:

• Introduction
• Vectors
• The Dot Product
• The Vector Product
• Gaussian Elimination
• The Matrix
• Determinants
• Rank
• Linear Mappings
• Eigenvalues and Eigenvectors

This is a simple introduction to linear algebra, and concepts are explained to the reader with the help of interactive visualizations. In an effort to make the subject easier to understand, this book makes topics more generalized and abstract, with examples provided in each chapter.

2. Computational Linear Algebra for Coders  — Course by FastAI

 
Unlike traditional linear algebra courses that teach you to solve linear equations manually, this learning track by FastAI will demonstrate the implementation of these techniques using a computer.

In this course, you will learn to perform matrix computations in Python with the help of libraries like Numba and PyTorch.

The best part of this course is that it takes a top-down approach to learning. While most math courses tend to focus on theory, FastAI’s linear algebra course will provide you with code examples and practical examples before diving into more complex details. 

The top-down approach makes it easier for students to focus, as they are able to work on interesting applications first before diving into the math-heavy content.

This course assumes that you have basic knowledge of linear algebra, so I recommend reading the textbook above as a pre-requisite before taking the course.

3. Linear Algebra  — MIT OpenCourseWare

 
This is a series of video lectures by MIT OpenCourseWare that has been made freely available to the public. There are 34 video lectures in this course taught by Prof. Gilbert Strang, whose teaching style is intuitive and will provide you with a different outlook on problem-solving.

Each section comes with a problem set, and I’d recommend solving the problems for each lecture before moving on to the next. 

If you find that the problem set isn’t sufficient and that you lack practice, you can complement this course with its accompanying textbook (written by the same professor) — Linear Algebra and its Applications. However, keep in mind that while the course is available for free, the book comes with a cost. 

 
The resources above are a great way to familiarize yourself with the linear algebra behind machine learning algorithms. 

However, if you find it difficult to get through the material above, I suggest starting out with some lighter content such as 3Blue1Brown’s or Khan Academy’s linear algebra course. These videos are created for complete beginners to math, and will serve as an easy introduction to the subject before you move on to deeper material listed above.

 
 
Natassha Selvaraj is a self-taught data scientist with a passion for writing. You can connect with her on LinkedIn.