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No bullshit guide to linear algebra
Linear algebra is the foundation of science and engineering. Knowledge of linear algebra is a prerequisite for studying statistics, machine learning, computer graphics, signal processing, chemistry, economics, and quantum mechanics. Indeed, linear algebra offers a powerful toolbox for modelling the real world.
The NO BULLSHIT guide to LINEAR ALGEBRA shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy.
The author has 15 years of tutoring experience, a B.Eng. in electrical engineering, a M.Sc. in physics, and a Ph.D. in computer science from McGill University.
Preview: https://minireference.com/static/exce...
Free tutorial: https://minireference.com/static/tuto... (4pp, PDF)
The NO BULLSHIT guide to LINEAR ALGEBRA shows the connections between the computational techniques of linear algebra, their geometric interpretations, and the theoretical foundations. This university-level textbook contains lessons on linear algebra written in a style that is precise and concise. Each concept is illustrated through definitions, formulas, diagrams, explanations, and examples of real-world applications. Readers build their math superpowers by solving practice problems and learning to use the computer algebra system SymPy.
The author has 15 years of tutoring experience, a B.Eng. in electrical engineering, a M.Sc. in physics, and a Ph.D. in computer science from McGill University.
Preview: https://minireference.com/static/exce...
Free tutorial: https://minireference.com/static/tuto... (4pp, PDF)
550 pages, Paperback
First published March 1, 2014
72 people are currently reading
723 people want to read
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Displaying 1 - 12 of 12 reviews
March 26, 2021
A mix of academic rigour and mathematical intuition. The author knows which concepts should be stressed and repeats them over many chapters. The best part is that the author provides applications in the real-world with an entire chapter dedicated to it, which reinforces the understanding. I would recommend watching 3blue1brown's linear algebra videos along with it.
August 21, 2020
It finally clicked. All it took was this one book. If only that's how they taught linear algebra in college...
July 13, 2019
It's a brilliant book to understand LA. It provides the basic foundation needed to understand more advance topics in LA and related fields like ML, physics, and CS.
May 9, 2022
The book is like the title, no bullshit.
I have to say that there are a few times I almost wanna give up, then the author will say a few encouraging words at those moments: “you could understand it with what you just learned. “ I am glad that I trusted the author, and I learned a great deal. Sometimes, the biggest barrier is not intellectuals but emotions.
I really like the geometric algebra chapter, the intuition is amazing. Change of basis is another difficult topic to understand, the author did a fairly good job. The SVD chapters are mind-blowing. Chapter 3-5, I read quite a few times to fully get it.
Many application of linear algebra are not relevant to my research, but I was able to follow and learned something new and interesting, such as the cryptography, Bayesian networks.
For serious learners, I would recommend pairing this book with additional exercises (or coding questions) or books. This book has some exercises, but they are not enough to fully check your comprehension.
I have to say that there are a few times I almost wanna give up, then the author will say a few encouraging words at those moments: “you could understand it with what you just learned. “ I am glad that I trusted the author, and I learned a great deal. Sometimes, the biggest barrier is not intellectuals but emotions.
I really like the geometric algebra chapter, the intuition is amazing. Change of basis is another difficult topic to understand, the author did a fairly good job. The SVD chapters are mind-blowing. Chapter 3-5, I read quite a few times to fully get it.
Many application of linear algebra are not relevant to my research, but I was able to follow and learned something new and interesting, such as the cryptography, Bayesian networks.
For serious learners, I would recommend pairing this book with additional exercises (or coding questions) or books. This book has some exercises, but they are not enough to fully check your comprehension.
March 27, 2023
Not a beginner's book nor introductory text. Ivan Savov's book is best for readers who have had similar material in the past and/or have recently completed U.S. high school math (basic algebra, set theory, linear functions, quadratic equations, geometry, trigonometry). The first chapter reviews these subjects, then starts in on linear algebra in chapter 2, page 131. Savov dedicates the last three chapters to applications in industry, probability, and physics, eg, Google's PageRank.
Savov includes references to helpful online sites such as SymPy, https://www.sympy.org/, and Grant Sanderson's superb mathematics visualization videos, https://www.3blue1brown.com/. Use them to explore and expand on the text.
If you, like me, are looking to brush up on your general and applied math, get this book and work through it.
Savov includes references to helpful online sites such as SymPy, https://www.sympy.org/, and Grant Sanderson's superb mathematics visualization videos, https://www.3blue1brown.com/. Use them to explore and expand on the text.
If you, like me, are looking to brush up on your general and applied math, get this book and work through it.
April 15, 2026
It may be best to begin with this book’s weakest element, and that is the title: No Bullshit Guide to Linear Algebra. The title implies that this book is fluffy, that it is not a serious book on mathematics; and that is not the case. I hesitated to buy this book because of its title.
This is a book on linear algebra, the branch of mathematics whose central object is the matrix. Of its nine chapters, the first chapter—the longest—covers algebra of the sort the reader likely studied in high school. If your knowledge of the fundamentals is sound, you can safely skip over this chapter. But don’t do that. Why not? There are several reasons. First, you may find something in there that you don’t already know. You don’t know everything. You wouldn’t want to miss it. Also, it can be useful to see a new perspective, to observe from a new vantage point how things all fit together. The author is disciplined and thoughtful in his use of notation and the first chapter is where things are first introduced. But, aside from all that, the text is genuinely well written. Good writing is a pleasure to read and there is no reason to deny yourself.
The next five chapters present the contents of linear algebra proper. This treatment is thin on rigorous proof. But, rigorous proofs are not particularly useful for creating comprehension and building intuition. What you do find here are well-crafted descriptions and thoughtful explanations, many of a very high quality. Some give a uniquely useful perspective. Also, despite its only taking 230 pages, this material goes beyond the basics and includes advanced topics, i.e., fancy stuff.
The last three chapters cover applications with one chapter devoted to probability and the final chapter to quantum mechanics. Fourier transforms are covered in the catch-all chapter. If a book’s ending is its destination, then that destination would be quantum computing and quantum information theory. That may not be the reader’s destination and that’s fine. As a personal note, I had read Feynman’s original quantum computing paper some time ago, but it didn’t really come together for me until Savov supplied the missing pieces that Feynman had not made clear—or at least not clear enough to me.
I must admit that, in these final chapters, the author sometimes allows himself a fig leaf’s worth of coverage for a volume’s worth of subject. Thus, it becomes harder to read in places and I didn’t always come away with the sense of crystal clarity that I took away from the earlier chapters. The author gives many pointers out for further exploration. In fact, those appear throughout the book.
If there were to ever be a third edition, any revision should certainly proceed from back to front. There are elements early in the book that should be trapped in amber and preserved for eternity, just as they are. But, as for the last section? If the applications section were expanded, perhaps tripled, so as to provide for longer explanations, I’m not sure it would still be a linear algebra book. The applications section already runs long, relative to the central part of the book. Likewise, removing any of this in the interest of brevity would be a tragedy. So, it is as it is meant to be.
I hope there are more works forthcoming from Ivan Savov.
https://raspberrypi.tailcd13e6.ts.net...
This is a book on linear algebra, the branch of mathematics whose central object is the matrix. Of its nine chapters, the first chapter—the longest—covers algebra of the sort the reader likely studied in high school. If your knowledge of the fundamentals is sound, you can safely skip over this chapter. But don’t do that. Why not? There are several reasons. First, you may find something in there that you don’t already know. You don’t know everything. You wouldn’t want to miss it. Also, it can be useful to see a new perspective, to observe from a new vantage point how things all fit together. The author is disciplined and thoughtful in his use of notation and the first chapter is where things are first introduced. But, aside from all that, the text is genuinely well written. Good writing is a pleasure to read and there is no reason to deny yourself.
The next five chapters present the contents of linear algebra proper. This treatment is thin on rigorous proof. But, rigorous proofs are not particularly useful for creating comprehension and building intuition. What you do find here are well-crafted descriptions and thoughtful explanations, many of a very high quality. Some give a uniquely useful perspective. Also, despite its only taking 230 pages, this material goes beyond the basics and includes advanced topics, i.e., fancy stuff.
The last three chapters cover applications with one chapter devoted to probability and the final chapter to quantum mechanics. Fourier transforms are covered in the catch-all chapter. If a book’s ending is its destination, then that destination would be quantum computing and quantum information theory. That may not be the reader’s destination and that’s fine. As a personal note, I had read Feynman’s original quantum computing paper some time ago, but it didn’t really come together for me until Savov supplied the missing pieces that Feynman had not made clear—or at least not clear enough to me.
I must admit that, in these final chapters, the author sometimes allows himself a fig leaf’s worth of coverage for a volume’s worth of subject. Thus, it becomes harder to read in places and I didn’t always come away with the sense of crystal clarity that I took away from the earlier chapters. The author gives many pointers out for further exploration. In fact, those appear throughout the book.
If there were to ever be a third edition, any revision should certainly proceed from back to front. There are elements early in the book that should be trapped in amber and preserved for eternity, just as they are. But, as for the last section? If the applications section were expanded, perhaps tripled, so as to provide for longer explanations, I’m not sure it would still be a linear algebra book. The applications section already runs long, relative to the central part of the book. Likewise, removing any of this in the interest of brevity would be a tragedy. So, it is as it is meant to be.
I hope there are more works forthcoming from Ivan Savov.
https://raspberrypi.tailcd13e6.ts.net...
February 25, 2024
I initially considered rating the "No BS Guide to Algebra" three stars, recognizing its merits yet feeling it fell short of greatness. However, appreciating the author's diligent effort to amalgamate diverse concepts and present them cohesively, I decided on a four-star review. The author's commitment to simplification is commendable, particularly for those with minimal background in the subject. The applications section on Linear Algebra was notably impressive, offering clear and practical insights.
Areas for Enhancement:
- The narrative sometimes experiences abrupt transitions, which could be smoothed to maintain the reader's engagement.
- While the author endeavors to simplify complex topics, incorporating historical anecdotes or a storytelling approach could enrich the text, making it not only informative but also engaging and memorable.
This book stands out for its approachable content and valuable application sections, making it a worthwhile read for beginners, albeit with room for narrative enhancement to elevate the reader's experience further.
Areas for Enhancement:
- The narrative sometimes experiences abrupt transitions, which could be smoothed to maintain the reader's engagement.
- While the author endeavors to simplify complex topics, incorporating historical anecdotes or a storytelling approach could enrich the text, making it not only informative but also engaging and memorable.
This book stands out for its approachable content and valuable application sections, making it a worthwhile read for beginners, albeit with room for narrative enhancement to elevate the reader's experience further.
June 29, 2023
This book has been of great value while studying advanced linear algebra. Ivan Savov does an excellent job addressing the vast amount of complex topics in an approachable and enjoyable way. The combination of intuition and rigid math notation gently guides the reader through the book. In the end, you get a solid grasp on linear algebra.
November 12, 2019
This book is a good reference for someone who needs to know linear algebra but won't be taking a full course on it. My only gripe is that some concepts could have been covered in a bit more depth, and some of the application chapters at the end seemed unnecessary.
February 27, 2019
Excellent. I skipped the chapter on QM though
September 15, 2023
Deeply cringe
August 24, 2025
3.5 stars.
Abandoned at Chapter 5 somewhere near change of basis subsection. The book started really well and it held my interest until it failed to do so at the point where it became clear the book and author didn't have anything interesting to say and it became more and more tedious (less visuals/geometric insights etc) and irritatingly many exercises had typo/wrong answer and I had to refer to the errata often. I am glad I did all the exercises in the chapters I had studied so far.
The author should be appreciated for his efforts and I am planning to revisit the book in the future from where I left off.
Abandoned at Chapter 5 somewhere near change of basis subsection. The book started really well and it held my interest until it failed to do so at the point where it became clear the book and author didn't have anything interesting to say and it became more and more tedious (less visuals/geometric insights etc) and irritatingly many exercises had typo/wrong answer and I had to refer to the errata often. I am glad I did all the exercises in the chapters I had studied so far.
The author should be appreciated for his efforts and I am planning to revisit the book in the future from where I left off.
Displaying 1 - 12 of 12 reviews