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Introduction to Linear Algebra (Gilbert Strang) 5th Edition

by Gilbert Strang (Author)
4.4 4.4 out of 5 stars 471 ratings
See all formats and editions
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 cryptography • A new chapter on linear algebra in probability and statistics. A dedicated and active website also offers solutions to exercises as well as new exercises from many different sources (including practice problems, exams, and development of textbook examples), plus codes in MATLAB®, Julia, and Python.
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  1. ISBN-10
    0980232775
  2. ISBN-13
    978-0980232776
  3. Edition
    5th
  4. Publisher
    Wellesley-Cambridge Press
  5. Publication date
    August 11, 2016
  6. Language
    English
  7. Dimensions
    7.7 x 1.3 x 9.2 inches
  8. Print length
    600 pages
  9. See all details
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Editorial Reviews

Review

Introduction to Linear Algebra, 5th Edition
by Gilbert Strang

Wellesley - Cambridge Press, 2016, ISBN 978-0-9802327-7-6, x+574 pages.
Reviewed by Douglas Farenick, University of Regina

Undergraduate mathematics textbooks are not what they used to be, and Gilbert Strang's superb new edition of Introduction to Linear Algebra is an example of everything that a modern textbook could possibly be, and more.
First, let us consider the book itself. As with his classic Linear Algebra and its Applications (Academic Press) from forty years ago, Strang's new edition of Introduction to Linear Algebra keeps one eye on the theory, the other on applications, and has thestated goal of "opening linear algebra to the world" (Preface, page x).Aimed at the serious undergraduate student - though not just thoseundergraduates who fill the lecture halls of MIT, Strang's homeinstitution - the writing is engaging and personal, and the presentation is exceptionally clear and informative (even seasoned instructors maybenefit from Strang's insights). The first six chapters offer atraditional first course that covers vector algebra and geometry,systems of linear equations, vector spaces and subspaces, orthogonality, determinants, and eigenvalues and eigenvectors. The next three chapters are devoted to the singular value decomposition, lineartransformations, and complex numbers and complex matrices, followed bychapters that address a wide range of contemporary applications andcomputational issues. The book concludes with a brief but cogenttreatment of linear statistical analysis.
I would like to stress that there is arichness to the material that goes beyond most texts at this level.Included are guides to websites and to OpenCourseWare, which I shallcomment upon later in this review. The final page lists "Six GreatTheorems of Linear Algebra." Chapter 7 begins with an informativeaccount of image compression, and would be wonderful material for an undergraduate student to present in a seminar to other students.

Strang's experience at writing and teachinglinear algebra is apparent in the layout of the typeset. Offset in bluetype are topic-specific headings that indicate what is contained in thecontent of the text to follow. For example, on page 5, after developingmaterial on linear combinations of vectors, we find the heading "TheImportant Questions." On page 149, after studying the null space, thereis a subsection with the heading "Elimination: The Big Picture." Eachsection contains the headings "Review of the Key Ideas," "WorkedExamples," "Problems," and "Challenge Problems." These sections areessential reading for the instructor, not just the student. The WorkedExamples include material such as the Gershgorin Circle Theorem, whilethe Problems and Challenge Problems offer the student a chance to master basic ideas and to think much more mathematically about the conceptsunder study. For example, Problem 29 of Chapter 6 asks for thecomputation of the eigenvalues of three matrices (not just genericmatrices, but matrices with structure and, thus, a chance to learnsomething about how the features of the matrix influence theeigenvalues), while Problem 39 of the same chapter asks for the possible values of the determinants, traces, and eigenvalues of the six 3 X 3permutation matrices. There is nothing here that can be said to be dry,uninteresting, or irrelevant; rarely does an undergraduate mathematicstext feel so alive as this one.

This review appeared in the Bulletin of the International Linear Algebra Society, IMAGE Vol.58 (2017) 18-19

Book Description

The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while also seeing many minor improvements and major additions.

Product details

  • Publisher ‏ : ‎ Wellesley-Cambridge Press; 5th edition (August 11, 2016)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 600 pages
  • ISBN-10 ‏ : ‎ 0980232775
  • ISBN-13 ‏ : ‎ 978-0980232776
  • Reading age ‏ : ‎ 1 year and up
  • Item Weight ‏ : ‎ 2.58 pounds
  • Dimensions ‏ : ‎ 7.7 x 1.3 x 9.2 inches
  • Customer Reviews:
    4.4 4.4 out of 5 stars 471 ratings

About the author

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Gilbert Strang

Gilbert Strang

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Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004.

Customer reviews

4.4 out of 5 stars
4.4 out of 5
471 global ratings
Page 482 Print Issue
4 Stars
Page 482 Print Issue
The book is good but page 482 has an issue in printing in some batch I suppose.The replacement arrived and it has the exact same issue. I stop bothering to keep requesting a replacement and accept it as is.
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Top reviews from the United States

inessa tribunko
5.0 out of 5 stars Very good book
Reviewed in the United States on August 7, 2023
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Very thorough and good textbook
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KT Cheng
5.0 out of 5 stars A great textbook for learning linear algebra
Reviewed in the United States on December 2, 2023
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Fast shipping and well packaging.
A famous textbook written by Prof. Strang, who teaches linear algebra at MIT for several decades, is recommended by my professor for self-learning linear algebra. This book comes with open-source videos available on the MIT OpenCourseWare.
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Amazon Customer
4.0 out of 5 stars Page 482 Print Issue
Reviewed in the United States on May 11, 2022
Verified Purchase
The book is good but page 482 has an issue in printing in some batch I suppose.
The replacement arrived and it has the exact same issue. I stop bothering to keep requesting a replacement and accept it as is.
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Amazon Customer
4.0 out of 5 stars Page 482 Print Issue
Reviewed in the United States on May 11, 2022
The book is good but page 482 has an issue in printing in some batch I suppose.
The replacement arrived and it has the exact same issue. I stop bothering to keep requesting a replacement and accept it as is.
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3 people found this helpful
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william scott
2.0 out of 5 stars Not Clear
Reviewed in the United States on October 12, 2022
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This is the first book I bought to teach myself linear algebra and it did not go well. I was so confused by the end of chapter 1 that I quit and wondered if I come to the end of my mathematical abilities. Last year, 2023, I tried again with a book by Kuldeep Singh and finished it a month ago. I went back to Strang's book to review the material and get another perspective and immediately became confused as to what he was saying.

The problem with this book is that the author goes too fast. When presenting a concept or an example to a student, one needs to do every step and explain why that step is being taken. Strang omits many intermediate steps, and does not explain how he gets from point A to B. He often does not define terms and the student is left confused as to what he is talking about.

I do not recommend this book unless one is exceptional in math and can make the conceptual jumps the author requires.
11 people found this helpful
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Henri Tuthill
5.0 out of 5 stars Wish there was a published solution key to the problems, given I am studying on my own.
Reviewed in the United States on September 27, 2021
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the online lecture series from MIT follows most of the material in the text. There too many golden tidbits e.g. definitions found in the problem sets that do not rise to the level of formal definitions in the development material e.g. Pascal Matrices, various types of matrices are fully defined in the problem sets but no to be found in primary material.
6 people found this helpful
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Enrique alsina massana
5.0 out of 5 stars Best introduction I have ever seen
Reviewed in the United States on March 26, 2023
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Professor Strang is fantastic
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saulo
3.0 out of 5 stars Linear algebra is computational
Reviewed in the United States on December 30, 2021
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I like how the book was straightforward and taught you the basics of linear algebra, but keep in mind, it is very computational, if you planning to be a pure math major, their a better book with proofs. If you doing any other major or applied math, then this book is perfect.
10 people found this helpful
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Bobbi Avery
5.0 out of 5 stars Highly demonstrative!
Reviewed in the United States on September 6, 2022
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Every subtlety fully confronted for the practical application of linear algebra.
One person found this helpful
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Top reviews from other countries

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Prashant Tiwari
5.0 out of 5 stars Great book to learn linear algebra, especially for ML
Reviewed in India on February 7, 2024
Verified Purchase
Book covers everything from basics you learn in 11th and 12th to bachelor's, especially for machine learning. Might look a bit expensive but worth every penny. It has hardcover and very thick pages with great binding.
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Prashant Tiwari
5.0 out of 5 stars Great book to learn linear algebra, especially for ML
Reviewed in India on February 7, 2024
Book covers everything from basics you learn in 11th and 12th to bachelor's, especially for machine learning. Might look a bit expensive but worth every penny. It has hardcover and very thick pages with great binding.
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One person found this helpful
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Caj
4.0 out of 5 stars So far I think it's good, but I have some problems...
Reviewed in Sweden on October 13, 2022
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For the most part, I think it's a good book that goes through a lot of concepts, though, I must agree with some previous reviewers in that, a lot of the stuff doesn't feel completely clear, like explained properly.

EDIT: After starting to watch the lectures while reading, I think this is a great resource. Unfortunately I should have been aware of that before writing this review, he's a great professor!
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Commande impossible, pas de livraison en Belgique.
5.0 out of 5 stars Ok
Reviewed in France on February 2, 2021
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Ok, bien reçu
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Luis Medrano
5.0 out of 5 stars Excellent book
Reviewed in Canada on September 30, 2019
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This book takes you step by step into most of linear algebra. Excellent book and professor
2 people found this helpful
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Shen
5.0 out of 5 stars Although accessible everywhere, but still good to get one
Reviewed in the United Kingdom on November 15, 2018
Verified Purchase
You may have heard or found related resources about this book many times before, so do I. But it does help me a lot as I have been stuck in many technical details on machine learning in depth, as I don't fully understand related linear algebra concepts. Besides, this hardcopy one is really good to read.
3 people found this helpful
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