Top Resources for Learning Linear Algebra for Machine Learning

 

How to Get Help with Linear Algebra for Machine Learning?

Linear algebra is a field of mathematics and an important pillar of the field of machine learning.

It can be a challenging topic for beginners, or for practitioners who have not looked at the topic in decades.

In this post, you will discover how to get help with linear algebra for machine learning.

After reading this post, you will know:

• Wikipedia articles and textbooks that you can refer to on linear algebra.
• University courses and online courses that you can take to learn or review linear algebra.
• Question-and-answer sites where you can post questions on linear algebra topics.

Let’s get started.

Overview

This post is divided into 6 sections; they are:

1. Linear Algebra on Wikipedia
2. Linear Algebra Textbooks
3. Linear Algebra University Courses
4. Linear Algebra Online Courses
5. Ask Questions About Linear Algebra
6. NumPy Resources

Linear Algebra on Wikipedia

Wikipedia is a great place to start.

All of the important topics are covered, the descriptions are concise, and the equations are consistent and readable. What is missing is the more human level descriptions such as analogies and intuitions.

Nevertheless, when you have questions about linear algebra, I recommend stopping by Wikipedia first.

Some good high-level pages to start on include:

• Linear Algebra
• Matrix (mathematics)
• Matrix decomposition
• List of linear algebra topics

Linear Algebra Textbooks

I strongly recommend getting a good textbook on the topic of linear algebra and using it as a reference.

The benefit of a good textbook is that the explanations of the various operations you require will be consistent (or should be). The downside of textbooks is that they can be very expensive.

A good textbook is often easy to spot because it will be the basis for a range of undergraduate or postgraduate courses at top universities.

Some introductory textbooks on linear algebra I recommend include:

Introduction to Linear Algebra, Fifth Edition, Gilbert Strang, 2016

• Introduction to Linear Algebra, Fifth Edition, Gilbert Strang, 2016.
• Linear Algebra Done Right, Third Edition, 2015.
• No Bullshit Guide To Linear Algebra, Ivan Savov, 2017.

Some more advanced textbooks I recommend include:

Matrix Computations

• Matrix Computations, Gene Golub and Charles Van Loan, 2012.
• Numerical Linear Algebra, Lloyd Trefethen and David Bau 1997.

I’d also recommend a good textbook on multivariate statistics, which is the intersection of linear algebra, and numerical statistical methods. Some good introductory textbooks include:

Applied Multivariate Statistical Analysis,

• Applied Multivariate Statistical Analysis, Richard Johnson and Dean Wichern, 2012.
• Applied Multivariate Statistical Analysis, Wolfgang Karl Hardle and Leopold Simar, 2015.

There are also many good free online books written by academics. See the end of the Linear Algebra page on Wikipedia for an extensive (and impressive) reading list.

Linear Algebra University Courses

University courses on linear algebra are useful in that they layout the topics that an undergraduate student is expected to know.

As a machine learning practitioner, it is more than you need, but does provide context for the elements that you do need to know.

Many university courses now provide PDF versions of lecture slides, notes, and readings. Some even provide pre-recorded video lectures, which can be invaluable.

I would encourage you to use university course material surgically by dipping into courses to get deeper knowledge on specific topics. I think working through a given course end-to-end is too time consuming and covers too much for the average machine learning practitioner.

Some recommended courses from top US schools include:

• Linear Algebra at MIT by Gilbert Strang.
• The Matrix in Computer Science at Brown by Philip Klein.
• Computational Linear Algebra for Coders at University of San Francisco by Rachel Thomas.

Linear Algebra Online Courses

Online courses are different from university courses.

They are designed for distance education and often are less complete or less rigorous than a full undergraduate course. This is a good feature for machine learning practitioners looking to get up to speed fast on the topic.

If the course is short, it may be worth taking it through end-to-end. Generally, and like university courses, I would recommend being surgical with the topics and dip in as needed.

Some online courses I recommend include:

• Linear Algebra on Khan Academy
• Linear Algebra: Foundations to Frontiers on edX

Ask Questions About Linear Algebra

There are a lot of places that you can ask questions about linear algebra online given the current abundance of question-and-answer platforms.

Below is a list of the top places I recommend posting a question. Remember to search for your question before posting in case it has been asked and answered before.

• Linear Algebra tag on the Mathematics Stack Exchange
• Linear Algebra tag on Cross Validated
• Linear Algebra tag on Stack Overflow
• Linear Algebra on Quora
• Math Subreddit

NumPy Resources

You may need help with NumPy when implementing your linear algebra in Python.

The NumPy API documentation is excellent, below are a few resources that you can use to learn more about how NumPy works or how to use specific NumPy functions.

• NumPy Reference
• NumPy Array Creation Routines
• NumPy Array Manipulation Routines
• NumPy Linear Algebra
• SciPy Linear Algebra

If you are looking for a broader understanding on NumPy and SciPy usage, the below books provide a good starting reference:

• Python for Data Analysis, 2017.
• Elegant SciPy, 2017.
• Guide to NumPy, 2015.

Summary

In this post, you discovered how to get help with linear algebra for machine learning.

Specifically, you learned about:

• Wikipedia articles and textbooks that you can refer to on linear algebra.
• University courses and online courses that you can take to learn or review linear algebra.
• Question-and-answer sites where you can post questions on linear algebra topics.

Do you have any questions?
Ask your questions in the comments below and I will do my best to answer.