Linear Algebra: Theory, Intuition, Code
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Are you ready to dive into the vibrant world of linear algebra and learn how it powers real-world applications? Welcome to this comprehensive textbook, where traditional theory meets modern computational practices.
Linear algebra is the magic behind many computational sciences — machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and more. But here’s a secret: the way it’s taught in traditional textbooks isn’t how professionals use it in the field.
For instance, have you ever wondered about the practical importance of a matrix’s “determinant”? You might be in for a surprise! This book bridges the gap between theoretical understanding and practical application, showing you not only the “what” but also the “how” of implementing linear algebra in real-world scenarios.
What makes this book a must-have resource?
- Crystal-clear explanations of linear algebra concepts and theories.
- Multiple angles to explain ideas, a proven technique to help cement your understanding.
- Vivid graphical visualizations to enhance your geometric intuition of linear algebra.
- Real-world implementations in MATLAB and Python. After all, in today’s world, you seldom solve math problems by hand. Software is the way forward!
- A range of topics from beginner to intermediate levels, including vectors, matrix multiplications, least-squares projections, eigendecomposition, and singular-value decomposition.
- Emphasis on the application-oriented aspects of linear algebra and matrix analysis.
- Intuitive visual explanations of diagonalization, eigenvalues and eigenvectors, and singular value decomposition.
- Ready-to-use codes in MATLAB and Python to bring linear algebra concepts to life on your computer. All codes can be downloaded from https://github.com/mikexcohen/LinAlgBook.
- A unique blend of hand-solved exercises and advanced code challenges. Remember, math is not a spectator sport!
Whether you’re just starting your journey in linear algebra or seeking to apply these concepts to data analyses on computers (such as data science, machine-learning, or signal processing), this book is your go-to guide. With this book at your side, you won’t just learn linear algebra; you’ll experience it!
35 reviews for Linear Algebra: Theory, Intuition, Code
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Proofs from THE BOOK
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. –
Excellent book to learn Linear Algebra from algebraic and geometric perspectives, with good examples and Python code. Read the book, do the paper and coding exercises. All exercises have solutions.
Avishek Sen Gupta –
Very nice book, which does not skip detailed explanations of why something should be so. The strength of this book is that for almost every important assertion, it adds at least a one-liner detailing why that is so. In all cases, it is then possible to jump back to the relevant section and brush up, in case you skipped something in your reading or understanding. This encourages people to potentially skip a topic or two and then comeback and familiarise themselves with it.
since there are no ” It is obvious that…” statements in the book, unlike many other, drier, textbooks, this one is ideal for self-study, with extra notes to link back to relevant results that you may have forgotten after a first reading.
The only thing I’d have liked to see is a more expanded explanation of PCA. The SVD chapter could have used more examples too. But, other than that, a top-notch introductory book to linear algebra. I’d rank it higher than Strang’s linear algebra books, which I also own.
marco antonio paes –
Poucos autores que se propõem a ensinar álgebra linear conseguem fazê-lo de maneira tão clara e eficiente.
Michael X. Cohen tem o talento nato de escrever bem e transmitir ideias e como o estudo da álgebra linear pede muita abstração só alguém com este talento para fazer um trabalho tão brilhante.
Quem quer se desenvolver na arte da matemática não pode deixar de conhecer melhor este autor e o resto do seu trabalho principalmente os cursos que ele oferece e que podem complementar muito bem o conteúdo deste livro.
Kate Lee –
Perfect and clear explanation with good examples. Very easy to follow. I love this book!
Shane Norris –
While having completed the Mathematics for Machine Learning: Linear Algebra course on Coursera I have still been finding the content of Mathematics for Machine Learning heavy going so made the decision to take a step back and sure up the foundations of my rudimentary linear algebra knowledge.
After making consideration between three texts: ‘Linear Algebra: Theory, Intuition, Code’ by Mike Cohen, ‘Introduction to Linear Algebra’ by Gilbert Strang, and ‘Linear Algebra’ by Jim Hefferon. I eventually pulled the trigger on MIke Cohen’s book based on a mixture of the breadth of topics covered in the table of contents, and the authors informal writing voice from what I could ascertain via the online opening chapter.
While it’s early day’s yet (have only just completed the first three chapters at present) from what I have read so far I am very pleased with the decision and looking forward to completing the text, a particular aspect that stood out to me was during chapter three while demonstrating a proof that the algebraic and geometric definitions of the dot product are equivalent, the author took the time to drill down and derive the Law of Cosines instead of just glossing over it’s inclusion and referring the reader back to the cobweb filled part of there brain where that particular fact may or may not have ever resided…
Just the thing for a reader such as myself looking to develop some intuition of the mathematics involved in ML but needs a little help filling the gaps in there fundamentals – but doesn’t have the time or inclination to return to school.
*TwinMama –
If I had this a college student back then, I probably would’ve done much better in Linear Algebra. I appreciate Dr. Mike X Cohen’s conversational style and sense of humor throughout the book. I could keep reading and practicing for hours without feeling too overwhelmed, needing a break. As stated in the book, one does not *need* to know coding to work through the book. While this is true, I wish I had gotten some familiarity with basic coding, especially Python, to get the most out of it.
N. Vadulam –
Tadej –
The book is really insightfull. It includes code in Python which for me was important and not just plain theory but also practical examples! A great buy, I really recommend it
cynthia peltier –
I just finished reading the entirety of this book and would highly recommend it to anyone doing a self-teach of linear algebra, especially if you’re more interested in the applied side of things.
The book is very approachable and doesn’t assume the reader has more than a background of high school algebra. My favorite part: the author focuses heavily on building long-lasting intuition. Each section is well motivated so that the reader will have an interest in moving through the book.
Ryan Zurrin –
I love this book, and the examples that allow us to use python and MATLAB really help me want to learn more and play around which is really what helps me in learning this stuff.
R. Frank –
This is the best book introduction to linear algebra I’ve ever read. The explanations are clear, concise, and with a sense of humor as well. The presentation is I. A very logical order, and unlike some other books, doesn’t get confusing by mixing in later topics with the current topic, as if you might already understand that future topic ( some of you might recognize the books I’m referring to here). Anyways, if you buy one book, or need a book to help explain the book you currently have to use in class, this is it.
_Set –
Hello…I am not too familiar w/ linear Algebra but I know enough to know I do not know what I am reading about currently. So, in hindsight, I should have educated myself slowly on Linear Algebra before getting to the first couple of Chapters in this book.
Although done in plain English and easily understood, it is almost unbelievable. Either this fellow, the author, knows a lot about the subject or I am way under educated on this subject. It is neat to know the ideas are relevant in source (coding), 2D and 3D and more axes, and also in mathematics. I am still having a hard time believing that things are this easy. So, even though my undereducated self is reading the content, I am stuck in disbelief on how useful this book may turn out to be currently.
So far, so good.
I am on 4.3 so far and reading away. This author makes the unbelievable easily understood. I remember this subject from years ago and I was unaware of how it related to planes, axes, and coding.
Seth
P.S. This is not a total slosh nor can I mentally believe everything I am reading so far, e.g. as I have not put it to use yet. I learn and then provide an order of workable objectivity. So, I will read and then do it. I am currently taking notes and readin’ the nice content. Enjoy!
Nitin –
This a great book at a very affordable price. Every section is explained in a clear and simple manner. In addition, there are problems and coding exercises with solutions to test your understanding.
Jim Patchell –
Seems to be a great book, BUT, I am blind, and Text to Speach is NOT enabled, so beware if you need this feature. I should have been more careful before I purchased, but this was the first book I ran across that did not have this feature. I would have given it one star for this, but that seemed silly.
Leeber Cohen –
This is a beautiful supplement to the on-line course taught by Mike Cohen. It is very helpful to read his chain of thought and have the printed out code. This course of linear algebra will provide you with a basic understanding of the math involved without be overwhelming. The mathematical rigor of the proofs can be debated. As an example see the algebraic proof of the Cauchy-Schwarz inequality on page 56. However, I doubt that most of the readers will find this problematic. If you are not familiar with Python or Matlab, there are basic tutorials online or workbooks that you should study first. The code challenges require some basic knowledge of coding. That being said the author is correct that the book can be read without testing all the enclosed code. The beauty of computers is that the geometry of linear algebra can be graphically understood. The computer also allows you to solve determinants and matrices without doing numerous calculations. Hopefully, the author will have a similar courses for differential equations, complex variables, and differential geometry. His online course makes linear algebra more easily understood and fun. As in music mathematical circuits in your brain should be developed early. This level of linear algebra could easily be taught in high school. The computer graphs are cool and will be appreciated by many. I though about taking off one star because the code should be downloadable. I always make mistakes typing it out. Mike X Cohen deserves our thanks.
Sylvester –
Systematically builds up on concepts along with regular testing of knowledge.
Sandeep Kavadi –
Simple & efficient.
Kevin –
I’m currently taking Linear Algebra and this book has taught me more than my professors lectures plus our actual book. Please, I beg you – to all like students – you should get this.It’s an amazing read, with occasional humour to keep you going. I would say there’s a lack of problems; however, I would say everything else overshadows it (don’t let this keep you from getting the book). The style of the book isn’t too formal either, so it feels as if you were talking to a human. Nothing beats the intuition and understanding the book gives you.I rarely write reviews, but this book has saved me. I’m a high schooler on his mom’s account, so I hope it shows that anyone can learn from this book.
Math Customer –
This book explain the theory of linear algebra in a intuitive way with sufficient examples.
Marcus –
In my opinion the author did a great job. I am through a couple of chapters and I enjoyed reading them a lot. The level of difficulty is not kept low but the author teaches it step by step with more text respectively descriptions than just in most maths books which to me often appear as collections of equations, definitions and diagramms.
Brian C. Hagerty –
This may be the best math-instruction book I have ever read. If you want to understand linear algebra, get this book. The author does everything right: explains his terminology, explains why results and facts matter, and provides solutions for all of the practice problems. I read the whole thing through and am now going to go back from the beginning and work through it carefully. Mastering this material will provide a huge benefit to anyone interested in machine learning. Next up, I plan to get all of his Udemy courses.
Molenaar –
Easy and very funny to read, great material, thank you.
KONSTANTINOS FOTOS –
Easy to read. Perfect for self-teaching and for anyone interested in applications of Linear Algebra.(Machine Learning)
NeanderthalTechMan –
And I’ve read a LOT of them (Strang, Axler, Lay, Shilov).
Ryan –
I read the first 50 pages of this book before writing this review. This is probably one of the most well-written mathematics boos I’ve come across. The style is conversational. The answers are inline, so you don’t have to jump constantly to the back of the book. The book warns readers of possibly confusing issues. It includes python and MATLAB code, though understanding either is not a requirement. The only issue I’ve had so far is that I’ve had to add the line
plt.show()
to the python code to get the graphs to display, but that line was not in the book. Different environments have different requirements. It was easy for me to troubleshoot. But perhaps someone with even less experience than I with Python would have stumbled.
Seneca reader –
This is a great book for someone like me who has been out of college for many years. That does not mean it is dumbed down. The material is well presented without being overly academic. Some math authors write like it would be beneath them to write without obfuscation.
Speck –
It’s engaging, with a measured pace, and is not so densely packed like some maths books can be. I find other books will make some statement of mathematical truth and you’re just expected to understand it and to remember it. Not here. Stuff is actually explained, and it’s explained gently like you’re a human being. Recommended.
Avin Seneviratne –
I genuinely love this author for having so much humor included in the book. I find formal mathematics textbooks to be very stuck up and unapproachable. But this book changes all of that. Thank you for writing such a great book!
Anonymous –
One must read this book if you want to clear your basics. Great applied book on algebra with many examples and questions.
Miguel Ángel Norzagaray Cosío –
Incluye el tratamiento matricial recomendado en la actualidad, así como casi todos los temas importantes en la práctica del Álgebra Lineal Numérica. Los códigos son sencillos pero de gran ayuda.
Nicholas Schlabach –
This is a very well explained textbook introducing linear algebra and it’s applications.
It is easy to understand with a gentle introduction.
I used it as a supplement for a second-semester college class. I am a math major and still found it full of useful information.
ABC –
This is a well-written, readily accessible book covering not only a broad range of standard LA topics but also specialized topics like PCA, often not covered in more traditional texts. In addition, this book is written to be practical for machine learning applications. Physically, the book is well-constructed and should serve for years students and those wishing to either brush up on LA or get an ML-centric view.
Math Customer –
Not bad.
sail4dream –
The content is well explained, but some part of the text looks not sharp
Roman –
I bought this book with no knowledge of linear algebra. I initially wanted to know how it could be used for my engineering classes as there were problems that needed ( as a potential solution) to solve it. Some people might see this book as “babying” as it explains concepts but I find that nothing is skipped or skimped over as other math textbooks can do. Maybe your person that intuitively knows when they skip through steps in the math but I prefer the step by step to see what I missed ( or could miss!). Highly recommend. I thought this book was great.