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# No Bullshit Guide To Linear Algebra Review

Last Updated on August 9, 2019

There are many books that provide an introduction to the field of linear algebra.

Most are textbooks targeted at undergraduate students and are full of theoretical digressions that are barely relevant and mostly distracting to a beginner or practitioner to the field.

In this post, you will discover the book “No bullshit guide to linear algebra” that provides a gentle introduction to the field of linear algebra and assumes no prior mathematical knowledge.

After reading this post, you will know:

• About the goals and benefits of the book to a beginner or practitioner.
• The contents of the book and general topics presented in each chapter.
• A selected reading list targeted for machine learning practitioners looking to get up to speed fast.

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. No Bullshit Guide To Linear Algebra Review
Photo by Ralf Kayser, some rights reserved.

## Book Overview

The book provides an introduction to linear algebra, comparable to an undergraduate university course on the subject.

The key approach of the book is no crap and straight to the point. This means a laser focus on a given operation or technique and no (or few) detours or digressions.

The book was written by Ivan Savov, the second edition of which was released in 2017. Ivan has an undergraduate degree in electrical engineering and a Masters and Ph.D. in physics and has worked for the last 15 years as a private tutor for math and physics. He knows the subject and where students encounter difficulties.

### No Prerequisite Math

What makes this an excellent book for the machine learning practitioner is that the book is self-contained. It does not assume any prior mathematics background and all prerequisite math, which is minimal, is covered in the first chapter titled “Math fundamentals.”

It is the perfect book if you have never studied linear algebra, or if you studied it in school decades ago and have forgotten practically everything.

### Exercises to Practice

Another aspect that makes this book great for machine learning practitioners is that it includes exercises.

Each section ends with a few pop-quiz style questions.

Each chapter ends with a problem set for you to work through.

Finally, Appendix A provides answers to all exercises in the book.

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1. Math fundamentals. Covers the prerequisite math topics required to start learning linear algebra. Topics include numbers, functions, trigonometry, complex numbers, and set notation.
2. Intro to linear algebra. An introduction into vector and matrix algebra, the very foundation of linear algebra. Topics include vector and matrix operations and linearity.
3. Computational linear algebra. This chapter covers the issues that you will encounter when you start to implement linear algebra and must deal with the operations at any kind of scale. Topics include matrix equations, matrix multiplication, and determinants. Some Python examples are given.
4. Geometric aspects of linear algebra. Covers the geometric intuition for vector algebra, which is quite common. Topics include lines and planes, projections and vector spaces.
5. Linear transformations. Covers the core fiber of linear algebra as Ivan describes it. Introduces linear transformations.
6. Theoretical linear algebra. Covers the last steps of matrix algebra prior to applications. Covers topics such as matrix factorization methods, types of matrices, and more.
7. Applications. This chapter covers an impressive list of applications of linear algebra to a range of domains from electronics, graphs, computer graphics, and more. An impressive chapter to make the methods learned throughout the book concrete.
8. Probability theory. Provides a crash course on probability theory in the context of linear algebra including Markov chains and the PageRank algorithm.
9. Quantum mechanics. Provides a crash course into quantum mechanics through the lens of linear algebra, a specialty area of the authors.

## Selections for Machine Learning Practitioners

The book is excellent, and I recommend reading it from cover-to-cover, if you’re really into it.

But, as a machine learning practitioner, you do not need to read it all.

Below is a list of selected reading from the book that I recommend to get on top of linear algebra fast:

• Concept Maps. Page v. A collection of mind-map type diagrams are provided directly after the table of contents that show how the concepts in the book, and, in fact, the concepts in the field of linear algebra, relate. If you are a visual thinker, these may help fit the pieces together.
• Section 1.15, Vectors. Page 69. Provides a terse introduction to vectors, prior to any vector algebra. Useful background.
• Chapter 2, Intro to Linear Algebra. Pages 101-130. Read this whole chapter. It covers:
• Definitions of terms in linear algebra.
• Vector operations such as arithmetic and vector norm.
• Matrix operations such as arithmetic and dot product.
• Linearity and what exactly this key concept means in linear algebra
• Overview of how the different aspects of linear algebra (geometric, theory, etc.) relate.
• Section 3.2 Matrix Equations. Page 147. Includes explanations and clear diagrams for calculating matrix operations, not least the must-know matrix multiplication
• Section 6.1 Eigenvalues and eigenvectors. Page 262. Provides an introduction to the eigendecomposition that is used as a key operation in methods such as the principal component analysis.
• Section 6.2 Special types of matrices. Page 275. Provides an introduction to various different types of matrices such as diagonal, symmetric, orthogonal, and more.
• Section 6.6 Matrix Decompositions. Page 295. An introduction matrix factorization methods, re-covering the eigendecomposition, but also covering the LU, QR, and Singular-Value decomposition.
• Section 7.7 Least squares approximate solutions. Page 241. An introduction to the matrix formulation of least squares called linear least squares.
• Appendix B, Notation. A summary of math and linear algebra notation.

This section provides more resources on the topic if you are looking to go deeper.

## Summary

In this post, you discovered the book “No Bullshit Guide To Linear Algebra” that provides a gentle introduction to the field of linear algebra and assumes no prior mathematical knowledge.

Specifically, you learned:

• About the goals and benefits of the book to a beginner or practitioner.
• The contents of the book and general topics presented in each chapter.
• A selected reading list targeted for machine learning practitioners looking to get up to speed fast.

Have you read this book? What did you think?
Let me know in the comments below.

Do you have any questions?

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### 4 Responses to No Bullshit Guide To Linear Algebra Review

1. Anthony The Koala March 9, 2018 at 1:25 pm #

Dear Dr Jason,
I like both of Dr Savov’s books, under the “No b/s…” series for both linear algebra and calculus & physics. I would say his books whet my appetite for the Python programming language. His webpage is at https://minireference.com/ . At the bottom of the page are “free” guides on mechanics, linear algebra, Sympy (for Python). There’s also a concept map connecting maths with physics.

A point about the books. The books are not exhaustive of the topics. For example in his Linear Algebra book there is not an exhaustive list of graphic interpretations such as 3D plane interpretations of what happens when there is no solution to the problem of not being able to solve a system of linear equations. You may need to look at other Linear Algebra books such as Anton’s “Elementary Linear Algebra” to fill in areas.

Nevertheless, i agree with Dr Jason in that it gets one “….on top of linear algebra fast.” and in plain English.

Regards
Anthony of Sydney NSW

• Jason Brownlee March 10, 2018 at 6:21 am #

Thanks Anthony.

2. AbsarF March 29, 2018 at 9:52 am #

Any plans for you to write a simple and basic concepts book on “Calculus” required for Machine Learning?

Thanks

• Jason Brownlee March 29, 2018 at 3:16 pm #

Yes, I hope to cover it in the future.