Top 5 Best Books on Linear Algebra

We all had to take algebra classes in grade school. Do you remember the term “linear algebra?” It is a specific branch of mathematics that deals with linear equations and linear functions. Almost every area of mathematics uses linear algebra to some extent.

For example, geometry utilizes linear algebra to define basic objects like rotations, lines and planes. If you’re planning to go into any career field associated with engineering, economics, physics, or any other type of science, then you’re going to be studying linear algebra quite extensively. Scientists depend on linear algebra to create models of natural phenomena, especially when it comes to computing them.

Since it is “linear,” that means linear algebra deals with straight line calculations and equations. That is why matrices and vectors are used to solve these problems. There is also non-linear algebra which deal unproportioned objects or lines. Linear, on the other hand, deals strictly with two perfectly proportional objects.

We know that linear algebra can be confusing, especially if you are not to keen on mathematics to begin with. But there are a number of good books on linear algebra. Some of these books are suitable for beginners while others are written specifically for experienced mathematicians and advanced algebra students.

To narrow down your search for the best linear algebra books, we’ve already done the hard work for you.

Our Best Picks

Below are the top 5 books on linear algebra:

1) Introduction to Linear Algebra: 5th Edition

“Introduction to Linear Algebra” is the fifth edition of the book written by Gilbert Strang. It was written specifically for people who are new to linear algebra. You will learn about matrices and the various linear equation systems that exist. It is clear from reading the book that the author understands mathematics very well. He even goes so far as to make comparisons between calculus and linear algebra.

In addition to linear algebra techniques, the author offers many examples of numerical methods and geometrical examples. You could literally learn a year’s worth of introductory linear algebra by absorbing all the information in this one book.

2) Linear Algebra and its Applications: 5th Edition

“Linear Algebra and its Applications” thoroughly goes over algorithms and applications at an introductory level. You could probably learn more about linear algebra just by reading this one book than you could in a classroom. The amount of material covered in the book is the equivalent of an entire semester’s worth of teachings in a traditional school setting.

Have you always wondered why linear algebra is important to learn and how it relates to the everyday world? The authors do a great job of explaining how linear algebra is actually utilized in various applications of engineering, science, and business. If you’re looking for a career in any of these fields, then you might want to pay attention to this book and what it has to teach.

3) No Bulls**t Guide to Linear Algebra

“No Bulls**t Guide to Linear Algebra” is a book title that you cannot help but love. It was written for beginner and intermediate level linear algebra students. The author, Ivan Savov, does not mess around with his explanations of linear algebra concepts and applications. He eliminates all the filler content that you’d find in other linear algebra books and just dives right into the step-by-step explanations of what you need to know.

Ivan uses clear, easy-to-understand English that even a layman person can comprehend. He even includes practice problems in every section so that people can test their newfound linear algebra skills along the way. These real-life problems of linear algebra go a long way in helping people to understand their usefulness in the real world.

4) Linear Algebra Done Right

“Linear Algebra Done Right” is an intermediate level linear algebra book. This is a strictly mathematical book that does not focus so much on applications, linear equation systems, and determinants. What it does focus on are linear operators in dimensional spaces that are finite rather than infinite.

The author, Sheldon Axler, tries to help the reader think about vectors and operators more than calculations. Any aspiring or advanced mathematicians will find this book to be interesting. It is written in a way that anyone can understand it. The author even includes full color graphics and sidebars to assist with the readers’ understanding of the concepts that are presented.

5) Advanced Linear Algebra: Third Edition

“Advanced Linear Algebra: Third Edition” is one of the more advanced linear algebra books on the market. It gives over the linear algebra theory in quite detail, both the classic theory and the modern theory. You should learn about each theory because it helps you differentiate the concepts of linear algebra. Then you can develop a better understand of the systems in general.

If you are not an advanced algebra student or mathematics student, then you probably won’t comprehend the information in this book all that well. There is a lot of highly technical language that only experienced algebra students can understand well. The author, Steven Roman, even talks about how standard undergraduate college students had trouble with the text.


Most people are not experienced enough in mathematics to comprehend a basic level of linear algebra. But if you truly want to learn linear algebra, then you should start with one of the first three books mentioned on this list. They were all written for beginners who have little to no knowledge of linear algebra.

Every advanced form of mathematics seems difficult at first. But if you continue to study linear algebra a little bit each day, then you’ll find that it’ll get easier as time goes on. Most mathematicians can vouch for this because understanding matrices and equations is not something we’re born with. It must be taught to us in a clear and concise manner.

Some books do a good job of doing that and some books do not. Everyone is different, so it is up to you to decide which one of these books is most right for your particular level of mathematics.

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