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Introduction to Linear Algebra, Fourth Edition [Hardcover]

by Gilbert Strang
3.6 out of 5 stars  See all reviews (54 customer reviews)

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Book Description

February 10, 2009 0980232716 978-0980232714 4
Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'.

Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, fourier methods and the FFT, linear programming, and computer graphics.

Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Complex Vectors and Matrices; Solutions to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell.

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Editorial Reviews

Book Description

A leading textbook for first courses in linear algebra. Instead of teaching students by repetitive drill, Gilbert Strang encourages students to real mathematical thinking; an approach that has been successful over many years at MIT. The book is supported by online lectures and learning material via

About the Author

Gilbert Strang is a Professor of Mathematics at Massachusetts Institute of Technology and an Honorary Fellow of Balliol College, of the University of Oxford, UK. His current research interests include linear algebra, wavelets and filter banks, applied mathematics, and engineering mathematics. He is the author or co-author of six textbooks and has published a monograph with George Fix titled “An Analysis of the Finite Element Method.” Professor Strang served as SIAM’s president from 1999-2000, chaired the U.S. National Committee on Mathematics from 2003–2004, and won the Neumann Medal of the US Association of Computational Mechanics in 2005. He is a fellow of the American Academy of Arts and Sciences.

Product Details

  • Hardcover: 584 pages
  • Publisher: Wellesley Cambridge Press; 4 edition (February 10, 2009)
  • Language: English
  • ISBN-10: 0980232716
  • ISBN-13: 978-0980232714
  • Product Dimensions: 9.2 x 7.7 x 1.3 inches
  • Shipping Weight: 2.6 pounds (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (54 customer reviews)
  • Amazon Best Sellers Rank: #16,201 in Books (See Top 100 in Books)

More About the Author

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

Most Helpful Customer Reviews
205 of 221 people found the following review helpful
5.0 out of 5 stars Opinion of a 35-year veteran professor April 14, 2009
I write as a 35-year veteran teacher of mathematics and statistics, at Mount Holyoke College. This semester I am teaching two sections of linear algebra, from Gilbert Strang's Introduction to Linear Algebra, 4th edition. I understand that I'm one of the first, perhaps the very first, to teach from this edition, scooping even the author himself, whose spring semester at MIT began a week after Mount Holyoke's.

In choosing a book for my course, I reviewed more than a dozen choices. In what follows, I'll try to set out why, looking back on the first two-thirds of the semester, I'm firmly convinced that I chose the right book to teach from. But first, here's an excerpt from an e-mail I sent the author a few weeks ago:

I've admired your book ever since the first edition came out, but
in our department we have to wait in line to teach linear algebra,
and this is my first chance to teach from your book. It's hard to
put into words how much I'm enjoying it.

In 35 years, I've nearly always ended up feeling deeply disappointed
with almost any textbook I've tried to teach from. However I've
had the good fortune to find two books I really admire. Yours is
one of those two inspiring books. Thanks to you, I'm having a blast!

Enthusiasm aside, I'll start the substance of my review with four questions, aimed both at students and at teachers. These questions highlight the features I find inspiring - but they are not merely rhetorical: I've tried to formulate questions that should be helpful to anyone trying to decide whether Strang's Introduction to Linear Algebra is the right choice for them. In each instance, although my own answer is a resounding "Yes to choice one!
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51 of 54 people found the following review helpful
5.0 out of 5 stars Great for the Newcomer, Probably too Slow for Familiar November 27, 2010
By jdg
Format:Hardcover|Verified Purchase
I bought this book (the 3rd edition of it) my sophomore year as an undergraduate engineer. I read a couple of sections and then got distracted and didn't pick the book up again until my first year as a graduate student. Before reading this book, my experience with linear algebra had been modest (much to the fault of my undergraduate curriculum), but I soon realized how important linear algebra is to an engineer.

This book was wonderful! I read nearly the entire thing over the course of a month (working a large number of the problems), and since then have referenced it often. The chapter on Eigenvalues, Linear Transformations, and Applications are extremely useful (in the 3rd edition 6,7, and 8). Strang's style is refreshing in the world of dry math books; he really gives you the intuition and excitement behind the math. I find this invaluable as an engineer.

There is a downside to this: the book is wordy for a math book and the key results scattered throughout the text. For this reason I would highly recommend this book for someone without much background in linear algebra, but probably would not recommend it to someone looking for a refresher--a more succinct book would probably be more appropriate. I would also not recommend this book for someone interested in formal mathematics: the book claims informality, and it certainly is informal. That being said, most of the essential proofs are there in spirt, just not set down formally like many other math texts I have used.

I gave the book 5 stars because, although it isn't for everybody (no book can be), it is exactly what it claims to be: an INTRODUCTION to linear algebra, and an excellent one at that.
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30 of 31 people found the following review helpful
5.0 out of 5 stars The best part about this book December 8, 2009
Format:Hardcover|Verified Purchase
as an earlier reviewer pointed out, the best part of this book is that it follows along perfectly with Strang's free lecture series [...]
with lecture notes, assignments and of course the video lectures. When I you look at all the "value added" textbooks with CD's full of unhelpful material that takes more time to use than the benefit it gives, compare it to the pairing of this book with the online material, which together make a great learning experience.
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17 of 18 people found the following review helpful
5.0 out of 5 stars Nothing better November 8, 2009
By S. Vyas
Format:Hardcover|Verified Purchase
I had a very poor background in Linear algebra and I had a really advance optimization course. This book along with MIT opencourseware 18.06 (the course Prof Strang teaches at MIT) saved my semester. OCW is free. I went through some important video lectures and almost the whole book. Very simple english, covers all the basics, tells a bit about Matlab, has a chapter on engineering application examples(didn't go through that part). If you get confused regarding something in the book, which in very few cases you might if your running though it like I did, watch the related lecture and then go back to the book. You'll get the BIG PICTURE... I did. Thank you Prof. Strang.
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10 of 12 people found the following review helpful
4.0 out of 5 stars Decent but not fantastic July 2, 2010
By Xiao Hu
Format:Hardcover|Verified Purchase

1.The coverage of the four fundamental spaces is fantastic. The pictures showing their dimension, orthogonality etc is very very good and easy to remember. And the importance of the understanding of this topic can not be over emphasized. Prof Strang did an excellent job here.
2.The on-line lectures are excellent. Well at least for most of them.


The SVD part is not excellent. Prof. Strang agrees that this is the climax of linear algebra. But the presentation of this critical topic is not excellent. The link between the four fundamental spaces and SVD is not so clear. And the related pseudo-inverse is also not so excellent. Unfortunately, the video on SVD also suffers from the same problem. But I would not blame too much on the video. After all, I am not sure if an excellent coverage of SVD can be given within one lecture. But the book should have plenty of space for a good coverage.

For a good SVD coverage, I found the following is good.
1) A good understanding of the four fundamental spaces is very important. Prof. Strang does an excellent job in his book.
2) Some internet articles actually provide good introduction, better than those provided in books
3) An article on-line by Dan Kalman is very comprehensive but not the first thing you should read.
4) Trefethen in his Numerical Linear Algebra has some good (but not complete) description.
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Most Recent Customer Reviews
2.0 out of 5 stars Terrible book
Maybe I'm just too dumb to do linear algebra properly, but this book taught me nothing. I was taught half the book in a couple of hours by a friend who was better at linear algebra... Read more
Published 19 days ago by Yang Liu
5.0 out of 5 stars Of the two textbooks I have, it's the best
I have two linear algebra textbooks, one by McGraw Hill, and this one. I like both of them, but I like how this one is structured more. Read more
Published 1 month ago by Tuan Nguyen
5.0 out of 5 stars Clarity, insight, and a different approach
Mr Strang has a wonderful way of approaching the teaching of Linear Algebra. Though I took the subject in College (MANY years ago), I've not had a lot of opportunity (until... Read more
Published 1 month ago by Mitch Oldroyd
5.0 out of 5 stars Excellent textbook for an introduction into Linear Algebra
Really one of the best presentations for understanding linear algebra without getting bogged down in detailed proofs or unnecessary abstractions. Read more
Published 1 month ago by krishnan unnikrishnan
3.0 out of 5 stars Insight, 5 stars. Typing and style, 1 star
I *HIGHLY RECOMMEND* this book to anyone who wants to see into the insight and learn the essences of linear algebra. The reasons:

1. Read more
Published 2 months ago by Sen Peng Eu
2.0 out of 5 stars Eh.
Kind of hard to understand. Vocabulary used is sometimes somewhat contradictory. Besides that I guess it's good. Read more
Published 2 months ago by Jesus
1.0 out of 5 stars International Version
Instead of a blue book, I received a black book and quickly realized that I had received the international version of this book ):
Published 3 months ago by sosung
5.0 out of 5 stars This is how you get your books cheap.
Thanks for a good deal. Cllige would be realy expansive other wise. Thank you and don't stop selling books for school.
Published 3 months ago by simon b.
2.0 out of 5 stars A difficult book
Just re-iterating what a lot of people have said here. Since this book has seen a lot of uses clearly there are people out there who like the style. Read more
Published 3 months ago by Jason Dancks
3.0 out of 5 stars Not what I was looking for.
I bought this book as reference and supplement material for my class. I would like to know see the rigorous proof of theorems, since my professor is strict on the proof and proofs... Read more
Published 5 months ago by Charles
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