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11 Best Books To Learn Linear Algebra for Beginners (2022!)

Jamey Muller
Updated: March 31, 2022
5 min read

Linear Algebra is a branch of mathematics that studies vector spaces and the different methods for solving systems of linear equations. These methods include direct geometric representation, determinants, eigenvalues, and eigenvectors. In short, Linear Algebra is one of the most difficult math subjects to learn!

Let’s dive straight into our list of the 11 best books to help you learn and master linear algebra in no time!

At A Glance: The 3 Best Books to Learn Linear Algebra for Beginners

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Top pick
Linear Algebra and Its Applications
Linear Algebra and Its Applications

Linear Algebra and Its Applications is a straightforward textbook for a one-semester linear algebra course that emphasizes algorithms and applications.

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Despite the no-nonsense approach, it is a lengthy book covering everything that would typically be covered in an introductory course and a lot that would not. There is much more information here than a semester could cover.

The variety of applications is particularly impressive: although most of them use relatively simplified models of the object being studied, they provide a solid knowledge of how linear algebra is applied in practice. The applications include a wide range of scientific, business, and engineering topics, with many examples of dynamic systems.

Numerous notes on numerical aspects are also included. None of this goes into enough detail to make you an expert (which would be impossible in a one-semester beginner course) or even capable of tackling such problems on your own, but it does give you a decent idea of how and why linear algebra is utilized.

Note: We have also compiled a list of the 11 best calculus textbooks and have written about 9 things you should know when learning calculus.

Runner up
Linear Algebra: Step by Step
Linear Algebra: Step by Step

Both scientific and technological applications need linear algebra. With this full-course book, you can begin learning right now. It explains all of the essential principles of algebra in a consistent way, from basic to advanced.

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Without the help of a teacher, you will be able to grasp the topic thanks to the dynamic and interesting writing style. The broad range of questions, answers, keynotes, and step-by-step writing techniques make it the ideal linear algebra book for self-study. You can learn everything in a simplified form since it focuses extensively on algorithms and applications of linear algebra.

The author is well-versed in a wide range of topics. He was more constructive than others in his explanations of determinants, coordinate transformations, linear spaces, unitary spaces, finite-dimensional algebra, and their representations.

He also gave a clear picture of Euclidean spaces, quadratic forms, linear functions with vector arguments, the canonical form of the matrix, and other basic concepts. The author focused on a few key chapters in order to introduce you to algebraic structures and linear operations.

Also great
Introduction to Linear Algebra (Gilbert Strang)
Introduction to Linear Algebra

Gilbert Strang’s Introduction to Linear Algebra is a good and easy introduction to the discipline, with the author starting with a concise and passionate explanation of the principles of linear algebra.

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This is an intelligent and argumentative introduction to linear algebra, emphasizing matrices and linear equation systems. The author takes a broad perspective on linear algebra and sometimes incorporates calculus, Fourier series, function spaces, and wavelets, but the approach is usually efficient.

The book is heavy on linear algebra techniques, with almost unlimited examples of LU-decomposition and other numerical work and a lengthy Chapter 9 on numerical techniques.

However, the book does a fantastic job of going up and down between multiple levels of abstraction, depending on whatever level makes the subject at hand simpler to understand, and geometrical illustrations and rotations play a big part in the exposition.

#4
No bullshit guide to linear algebra
No Bullshit Guide to Linear Algebra

The No Bullshit Guide to Linear Algebra is a well-written and straightforward introduction to linear algebra.

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This book can help you understand the principles of linear algebra in a productive way. The author is thoroughly knowledgeable about all topics covered in such a brainstorming session. He didn’t cut any corners when it came to covering all of the strategies and secrets for mastering the core materials.

This book will teach you all you need to know in order to succeed in your academic exams. Every chapter includes highlighted key points and detailed theories to help you understand what’s going on.

This book is completely devoid of filler. Every section dives straight into the topic and takes you through it step by step until you’ve grasped everything. Nothing is left out, and everything is conveyed in conversational English that is clear, easily readable, and understandable.

Every section is jam-packed with practice problems so you can double-check your learning, and the author doesn’t skimp on the solutions by simply providing answers to a few of them.

The answer key includes the answers to all of the questions. He’s also taken the time to refer readers to valuable YouTube videos related to the information in the segment, which is great time-saving. He also includes numerous chapters with real-life examples.

#5
Linear Algebra Done Right (Undergraduate Texts in Mathematics)
Linear Algebra Done Right

This book, which is one of my favorites on linear algebra, can be regarded as a very pure-math version of the subject, with no applications and no work on determinants, matrices, or systems of linear equations.

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It’s a comprehensive presentation that will offer you an intuitive understanding of linear algebra from both algebraic and geometric perspectives, and it’ll keep your interest until the end. Each chapter includes a range of intriguing examples and tasks to help you grasp and manage the concepts of linear algebra.

The title of the book is not as bold as it seems; “done right” refers to a very sophisticated method of avoiding determinants. On the other hand, avoidance has the advantage of forcing you to think in terms of vectors and operators rather than a slew of calculations.

Axler has come up with several slick examples of things that would normally need a lot of grinding, which makes the book intriguing for mathematicians in and of itself. The book is very well-written and reads at a leisurely pace. It features a number of sidebars and incidental illustrations and is printed in full color.

#6
Linear Algebra (Dover Books on Mathematics)
Linear Algebra (Dover Books on Mathematics)

You can broaden your thinking abilities and brain functioning using this book. It’s a university-level book that’s great for deepening your understanding of mathematics.

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This comprehensive linear algebra textbook covered all of the material in a straightforward, concise, and informative way.

You could easily understand the formulas, ideas, and key points. Some practical methods are presented to help you become well-versed in a short period of time. This self-study book provides a plethora of examples with detailed solutions to help you improve your problem-solving abilities.

The logical and clear proofs are one of the book’s best characteristics. It will motivate you to develop practical math skills. This fantastic book will help you get a solid grasp of finite-dimensional algebras and their representations.

The book will educate you about the system of linear spaces, linear equations, linear functions of a vector argument, and determinants, among other topics. Aside from that, you’ll be immersed in a sea of bilinear and quadric forms, vectors, matrices, functions, and a slew of other topics.

#7
3,000 Solved Problems in Linear Algebra
3000 Solved Problems in Linear Algebra

For many people, learning by example is an effective method. This book offers 3000 solved problems that can be used to not only help students comprehend abstract ideas in linear algebra, but also as a complement to any linear algebra course.

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Solved problems range from basic questions to theorem proofs, and they can help you organize your thoughts and get a better understanding of the material.

The book is really clear and comprehensive, and it covers a wider variety of topics than you’ll find in a lower undergraduate class. If you devote enough time to this book, you will become an expert on the subject, with a far broader understanding of the subject and numerous diverse approaches to the same issue.

It will also help you in catching up on the little “details” that you may have absorbed during the period that you believed you would be tested on them, but which have since fled into the vacuum of forgotten math.

Because it solves problems similar to those found on exams, it will help you save time studying, improve your problem-solving abilities, and reach your personal best on exams.

Some other great books you can consider are:

#8
Linear Algebra: Theory, Intuition, Code
Linear Algebra: Theory, Intuition, Code

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#9
Linear Algebra (2nd Edition)
Linear Algebra 2nd Edition

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#10
Matrix analysis and applied linear algebra
Matrix Analysis and Applied Linear Algebra

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#11
Elementary Linear Algebra with Applications (9th Edition)
Elementary Linear Algebra with Applications

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Conclusion

Linear algebra is a complex subject that many people struggle with. The good news, though, is that there are plenty of books out there to help you learn and master linear algebra in no time!

We hope the 11 best books we’ve provided will give you some guidance on your journey towards mastering this challenging subject. As they say, “practice makes perfect,” so pick one of these books for an enjoyable challenge or use them all as study guides to explore different approaches to solving difficult problems.

Written by
Jamey Muller
I'm the head-writer @ Knowledge Eager (or, in plain English, I'm the guy writing the majority of the content here). Addicted to the stock market, football, sushi and tacos.
Have any questions? Write us a message.
Jamey Muller
I'm the head-writer @ Knowledge Eager (or, in plain English, I'm the guy writing the majority of the content here). Addicted to the stock market, football, sushi and tacos.