Best Linear Algebra Books For Self Study

Linear algebra is great application-based learning. It can be very technical and hence difficult to understand. Here, we would be discussing the best linear algebra books.

We would suggest you to start from the basics of such subjects as it will help build your interest and would help reach higher levels of understanding and practice. If done with the right approach, the subject as a whole can be very easily studied by yourself and without the need of others. However, the key would remain the choice of the right books, or else the learning can go wrong.

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Best Linear Algebra Books

Here are the best linear algebra books to self-study by yourself. 

Introduction to Matrices and Vectors by Jacob T. Schwartz

This is a book that helps every reader to practice the very basics of linear algebra. It will help strengthen the same concepts like matrices, inverses, etc., required as and when the level develops. All the topics that this book covers can be easily understood by anyone who is beginning to self-study linear algebra and may have a weak base or is unaware of the basic concepts of the subject.

introduction to matrices and vectors by jcob t schwartz

The book also covers the matrix systems required for linear algebra. 

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Linear Algebra done right by Shelfor Alexa 

This book is a must-read for anyone wanting to understand linear algebra. This is one of the best linear algebra books. The book can provide better explanations with examples that clear concepts from various geometric and other numerical perspectives.

linear algebra done right by shelfor alexa

The book gives a thorough practice and focuses on understanding central topics like the structure of linear operators. The level is up in this book and is excellent for self-study. 

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Matrix Analysis and Applied Linear Algebra by Carl D. Meyer 

If one has to excel at linear algebra, one must have practical experience and applied knowledge. This is important because it would teach you the actual life use of the subject. This book is best for this purpose and provides practical problem-based explanations and solutions. The book is wholesome due to its theory, applied components, and computational aspects.

matrix analysis and applied linear algebra by carl d meyer

For anyone doing self-study, this book will serve as a home tutor for you because of the way language is used in the book solely because of the author’s enriched experience. The book also has a lot about history and the formation of the subject as a whole. It deals with many current topics under linear algebra and has many questions that will challenge students to understand the section read better. 

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3000 solved problems in linear algebra by Seymour Lipchutz

Another one of the best linear algebra books. The subject demands a lot of problem-solving skills, and it requires a lot of numeric solving along with theory-based questions. A student needs to solve questions because they know where the level of their understanding is. This book is excellent for students to cover many linear algebra-based questions. It covers a lot of courses that are there for the subject. Since the book includes solutions, so a student will not get stuck.

3000-solved-problems-in-linear-algebra-by-seymour lipchutz

The questions in it range from simple ones to more complex ones demanding the use of multiple theories simultaneously. After completing this book, you can be sure of more excellent application and intuitive knowledge of the subject. The time that you take for one question would decrease. You will learn more than one approach for a particular question. Upon completing this book, your foundation would be solid that eventually, you will have the capacity to gain excellence in the subject.

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Theory and problems of linear algebra by Seymour Lipchitz 

This book has has been a go to for formal linear algebra courses for a long time. You would find it in many such institutions dealing with the subject. Therefore, the importance of this book is already set and is a must-read even if you are doing self-study. The book is very well put, which is why it is so popular.

theory and problems of linear algebra by seymour lipchitz

Being one of the best linear algebra books, the book has easy-to-read language and provides detailed descriptions, explanations, definitions, and even shortcuts to remember specific theories and principles. Like any formally used book, this book also has a series of numerical, many examples, and tests at the back of every chapter to test the students. The book also provides solved problems emphasizing details that the students might miss, which helps them know the slight mistake they might make, which jeopardizes their entire situation. Solved examples, thereby understanding back the theories and explanations. The book has widened its approach and tends to cover many more subjects, including computer science, mathematics, physics, quantitative analysis, etc. This can boost up the learning of the issue and at the same time stay in sync with the other institutions teaching formally.

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No bullshit guide to linear algebra by Ivan Savov

The title says it all aloud. If you’re a beginner, this is the perfect book for you to start in this area of the field and get to an intermediate level with its completion. This is one of the best linear algebra books. This book provides you with some valuable insights and explains every topic in a much detailed way so that you can easily grasp the idea behind any issue quickly.


Apart from this, the fun part about this book is that it also provides some real-life-based applications so that you can get a greater sense of why you should get started in the very first place. The author also provides some youtube recommendations to get the best out of the topic and make you feel confident in this area.

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Linear Algebra step by step – Kuldeep Singh

This book is a great learning source for students who are just getting started. With its wide variety of worked-out examples, questions, and proofs, it’ll give you a clear understanding of the problem statement guiding your way to approach the problem.linear algebra step by step kuldeep singh

It also gives you practical exposure rather than just theoretical knowledge. 

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Finite-Dimensional vector spaces 2nd edition by Paul Halmos

This is one of the best books for linear algebra. We recommend you have a basic knowledge of linear algebra before starting this book. However, it still works even if you’re not entirely familiar with the topic.

finite dimensional vector spaces 2nd edition by paul halmos

A bit more effort is from your side to understand the proofs and discussions of the algorithms as it’s not there in quite a depth in the book. On the other hand, the examples and questions are very insightful and will help you explore different possibilities of the concept.

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Is linear algebra the most difficult topic in maths?

No, as compared to the other topics like topology and abstract algebra, linear algebra is not the most difficult.

Is it possible to learn linear algebra with self study?

Yes, linear algebra is possible to be self-taught. There will be some topics that you would need help with, but with enough focus, it is possible.

Can I learn linear algebra without knowing algebra?

No, you need to know the basics before you start with the advanced algebra.

Is linear algebra more difficult than calculus 1?

Well, no calculus is harder than linear algebra.


These were our top picks to study linear algebra by yourself. Hope this list was helpful to you; happy learning!

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