The best textbooks for learning linear algebra

Prof. Strang has been teaching linear algebra at MIT for more than 60 years! This wealth of experience shines through in his book, which covers all the standard concepts using clear and concise explanations that have been polished through time and contain just the right amount of details.

The book is accompanied by a whole course of video lectures available through MIT OpenCourseWare or via YouTube. I learned a lot from Prof. Strang's approach to teaching; in particular, I appreciate the visualization of the fundamental theorem of linear algebra and his explanation of the matrix-vector product from the column picture and the row picture.

If you want to learn linear algebra, you can't go wrong with this classic.

In my opinion, Prof. Axler's book is the best way to learn the formal proofs of linear algebra theorems.

My undergraduate studies were in engineering, so I never learned the proofs. This is why I chose this book to solidify my understanding of the material; it didn't disappoint! Already, in the first few chapters, I learned new things about concepts that I thought I understood.

The book contains numerous exercises which were essential for the learning process. I went through the exercises with a group of friends, which helped me stay motivated. It wasn't easy, but all the time I invested in the proofs was rewarded by a solid understanding of the material.

I highly recommend this book as a second book on linear algebra.

I like Prof. Cohen's book because it includes computational examples based on Python and NumPy to illustrate each concept. This is the way I like to think about linear algebra concepts.

Yes, it's important to understand the formulas and theoretical ideas, but applying linear algebra operations in the real world will always involve some computational platform and not pen and paper. This is the only book I know that shows readers the practical computational linear algebra in parallel with the theory.

The author provides computational notebooks for each chapter on GitHub, which makes it easy to explore all the material from a code-first computational perspective.

This book has been a bit of an inspiration for me, and I use it regularly as a reference.

First of all, the content is complete and covers all the standard topics, including complete proofs. I like Heffron's book particularly because of the comprehensive exercises with complete worked solutions. It's hard to over-emphasize the importance of solving problems when learning, and this book has A LOT of them, which makes it an excellent choice for anyone learning on their own.

The author also provides lots of bonus material through his website, including slides, homework assignments, and a video lecture series. Last but not least, the entire book is released under an open license, allowing instructors to adapt and customize the material.

This is a good example of a book that makes a complicated topic accessible and easy to understand. Strictly speaking, this is not a linear algebra book, but quantum computing is so closely linked to linear algebra that I'm including this gem.

Prof. Wong covers all quantum computing topics in a straightforward and intuitive manner. He goes out of his way to prepare hundreds of examples of quantum circuits that made my life easy as a reader. What I like particularly about this book is that it explains all the derivations and all the details without skipping any steps.

I can recognize the work of a true master teacher: whenever I ran into a confusing concept, it was explained a few lines later, as if reading my mind.