Best Reference Books – Linear Algebra

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We have compiled the list of Top 10 Best Reference Books on Linear Algebra subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Linear Algebra along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Linear Algebra subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Linear Algebra" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Elementary Linear Algebra with Applications” by H Anton

“Elementary Linear Algebra with Applications” Book Review: Elementary Linear Algebra, gives an elementary treatment of linear algebra that is suitable for students in their freshman or sophomore year. The purpose is to present the fundamentals of linear algebra in the clearest possible way. A simple explanation is the main consideration. Calculus is a prerequisite along with there are clearly labeled exercises and examples for students who are studying calculus. Those exercises can help you strengthen your skills. There is no need for technology, if someone would like to use calculators with linear algebra capabilities, exercises have been included at the ends of the chapters that allow for further exploration of chapter’s contents.

2. “Linear Algebra and its Applications” by G Strang

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“Linear Algebra and its Applications” Book Review: This book is written in a student-friendly style and teaches real Mathematics. The student will experience a gear shift while going through it especially from the Introduction of Vector Spaces. Throughout the book, the theory is well presented, allowing students to have a deep dive from pure mathematics to applied mathematics. The exercises in the book are well designed and have many new problems added to it along with Singular Value Decomposition. Here a student can learn how the algorithm fits linear Algebra with an introduction to complex numbers. This book is a bonus for Computer Science students.

3. “Linear Algebra – A Geometric Approach” by S Kumaresan

“Linear Algebra – A Geometric Approach” Book Review: This book is highly readable, clear, and concise on Linear Algebra and is for undergraduate courses in mathematics. The key focus is on analytical geometry explanations to make a clear view of the topic. From the beginning, the topic is presented as simultaneous linear equations and their geometric interpretation which is the theme of the subject. Abstract algebraic concepts with geometric notions are a distinguishing feature of this book. It is designed such as to help students in Multivariable calculus and differential geometry. The explanation and concepts are well presented here.

4. “Advanced Engineering Mathematics” by E Kreyszig

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“Advanced Engineering Mathematics” Book Review: This book is well designed to let you taste the real cream of engineering mathematics and is also popular among Engineering students. This book is also a textbook of mathematics in various Engineering colleges as the problems in the books are so well designed that it will let you revise all your basic concepts in mathematics. This book is thoroughly updated and is streamlined to reflect the upliftment in the field. It covers all the advanced topics of engineering mathematics like Linear Algebra, Vector Calculus, Partial Differential Equation, Optimisation, Graphs, Complex Analysis, Statics & Probability so that students can relate to practical problems and can grasp their best.

5. “Introduction to Linear Algebra” by Gilbert Strang

“Introduction to Linear Algebra” Book Review: This book is well described and simple to Linear Algebra and has many breakthroughs within the subjects itself. This is an easy to read textbook that incorporates all the topics essential for detailed knowledge of the subject .The book teaches theory behind everything so it’s much engaging with the subject.The textbook includes many challenging problems for better grip on the topic .The book has been divided into seven different topics such as differential calculus, graph theory, statics, Fourier transformation methods, LPP and computer graphics and is complete for a deep overview of the subject.

6. “Linear Algebra: Step by Step” by Kuldeep Singh

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“Linear Algebra: Step by Step” Book Review: This book has a large number of examples and their step-by-step explanation for each topic. The topic is simplified in a way that allows distance learning with a concise solution to the set of problems freely available. This book consists of miscellaneous exercises at the end of each chapter which covers questions from past papers and also from various university exams helping the reader to boost his or her confidence. It also has short historical biographies of the leading players of Linear Algebra.This book is dynamic and has engaging style which includes question answer tests for the reader to make a clear view of the methods rather than rote learning. It also has exclusive interviews with the professionals who use the topic in their real life.

7. “Linear Algebra and Its Applications” by David C Lay and Steven R Lay

“Linear Algebra and Its Applications” Book Review: In this book, the traditional Linear Algebra texts are relatively easy to understand for students as the topic here is presented here in a familiar manner and with a concrete setting. Students often face problems with abstract topics like linear independence, spanning, subspace, vector space, transformations, and the book takes good care of this as the topic needs time to assimilate. These topics are important and understanding the topics is vital and this book makes it more accessible by its simple and explanatory demonstration which is easy to understand for students.

8. “Linear Algebra” by Georgi E Shilov

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“Linear Algebra” Book Review: In this book, the course has been made more accessible and useful. This book goes from the elementary level and easily catches up with advanced topics along with covering all the standard topics of an undergraduate or a beginning graduate course. The material here is demonstrated here in a simple style. Here the problems are included and their answers at the back. This book is good for students who want to learn techniques as it has an abundance of problems and examples so as to give the reader a good experience of applicability if the topic and is also useful for self-study and the classroom as well.

9. “Linear Algebra For Dummies” by Mary Jane Sterling

“Linear Algebra For Dummies” Book Review: This book is an easy to follow guide for the topic which offers a clear view of real-world application of Linear Algebra in many areas like programming, Engineering. This book is near a college-level linear algebra course, In which students study the basic operations and then abstract topics like vector space, linear transformation, determinants, and eigenvalues & vectors. This book gives students both theoretical and practical ways to solve different types of problems. The book presents the information in such a way that the reader can not only know how to solve it but also why to solve it.

10. “Linear Algebra Done Right” by Sheldon Axler

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“Linear Algebra Done Right” Book Review: This book for linear algebra is aimed at both graduate and undergraduate students. The narrative approach of this book to the topic focuses on the central goal of the topic so that students can understand the linear operations on finite-dimensional vector spaces. The book then deals with topics like linear maps, eigenvalues, and eigenvectors. Inner-product spaces, leading to the finite-dimensional spectral theorem and its consequences. In this book the concepts are concise and proofs are simple with a variety of interesting exercises on each chapter to help students in understanding the topic well and manipulate the objects of linear algebra. This book comes with many updated examples to illustrate the key ideas of linear algebra which include product spaces, quotient spaces, and dual spaces. There is no prerequisite for this book except mathematical maturity.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Linear Algebra – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Linear Algebra" so that one can readily see the list of top books on "Linear Algebra" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Linear Algebra subject, please let us know.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter