I've been teaching math and physics for more than 20 years as a private tutor. During this time, I experimented with different ways to explain concepts to make them easy to understand. I'm a big fan of using concept maps to show the connections between concepts and teaching topics in an integrated manner, including prerequisites and applications. While researching the material for my book, I read dozens of linear algebra textbooks and watched hundreds of videos, looking for the best ways to explain complicated concepts intuitively. I've tried to distill the essential ideas of linear algebra in my book and prepared this list to highlight the books I learned from.
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.
Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions, while at the same time seeing numerous minor improvements and major additions. The latter include: • A new chapter on singular values and singular vectors, including ways to analyze a matrix of data • A revised chapter on computing in linear algebra, with professional-level algorithms and code that can be downloaded for a variety of languages • A new section on linear algebra and…
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.
This best-selling textbook for a second course in linear algebra is aimed at undergrad math majors and graduate students. The novel approach taken here banishes determinants to the end of the book. The text focuses on the central goal of linear algebra: understanding the structure of linear operators on finite-dimensional vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra.
The third edition contains major improvements and revisions throughout the book. More than 300 new exercises have…
A dystopian tale about Tayler's brush with deadly augmented reality players who are out to kill him, and a wise cracking robot keen to take over the world.
As reviewer Joseph Sullivan from Aurealis magazine wrote, “Virtual Insanity will resonate with readers who enjoy modern takes on science fiction…
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.
Linear algebra is perhaps the most important branch of mathematics for computational sciences, including machine learning, AI, data science, statistics, simulations, computer graphics, multivariate analyses, matrix decompositions, signal processing, and so on. The way linear algebra is presented in traditional textbooks is different from how professionals use linear algebra in computers to solve real-world applications in machine learning, data science, statistics, and signal processing. For example, the "determinant" of a matrix is important for linear algebra theory, but should you actually use the determinant in practical applications? The answer may surprise you! If you are interested in learning the mathematical…
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.
The approach is developmental. Although it covers the requisite material by proving things, it does not assume that students are already able at abstract work. Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges. The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise each student's level of mathematical maturity.
Five days before the end of humanity, five unlikely heroes find themselves on an impossible quest to outlive the apocalypse.
5 Stars is the survival story of a mother and her baby facing impossible odds amidst a global apocalypse. Set in a dying world overseen by “The Neon God,” the…
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.
This is a short textbook that covers linear algebra topics clearly and concisely. The book starts with a review of high school math topics for adult learners who might need a refresher on the prerequisites. The book then covers all the essential topics of computational, geometrical, and theoretical linear algebra. Each concept is illustrated through definitions, formulas, diagrams, and lots of examples. The last three chapters of the book showcase linear algebra applications in computer graphics, signal processing, chemistry, economics, machine learning, and quantum physics.
This is the book for you if you need to (re)learn linear algebra and build a solid foundation for further studies in science and engineering.
It’s 2027. Rory O’Connor is the financial genius who helped create ICARUS, a quantum computer that controls the world’s stock markets with AI and algorithms. But Rory has recently suffered some tough breaks. He’s checked out of high finance and into a luxury Caribbean condo. After a former colleague finds…
A fast-paced literary thriller with a strong sci-fi element and loaded with existential questions. Beyond the entertainment value, this book takes a hard look at the perilous world of publishing, which is on a crash course to meet the nascent, no-holds-barred world of AI. Could these worlds co-exist, or will…