Introduction to Linear Algebra

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.

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 recently) to use it. I would always refer to my old college book when I needed a quick reminder. A flooded basement relieved me of my asset, so I purchased the book as a review/refresher/reference. My newly found need then pushed me into reviewing some of the material and I became very much attached to his methods of instruction. He has the ability to demystify the somewhat abstract move from simultaneous equations (taught earlier in the education) as well as move eloquently through the even more abstract concepts that make linear Algebra the 'basis' for a LOT of more advanced mathematics when used in today's computer age. New explanations of Spaces and Subspaces have now replaced my old concepts, and Eigenvalues and Eigenvectors are easier for me to explain now. If you're into image processing (or even 1D data processing), transforms and decompositions will be your friend, and Mr. Strang's explanations will help you get a firm grasp on them. Well worth the purchase (especially for a review/refresher/reference book).

Pros: 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. Cons: 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.

I used this book as self study. I was drawn to Gilbert Strang because it seemed to be the gold standard for linear algebra and the popularity is deserved. The one thing I would like to add is the effect of the use of symbolic math software. I used Mathematica but Strang has some code for Mathlab in the book. People have views on this subject but I find that Mathematica does the job well enough. The effect on me is that it made me feel a little insecure by not doing it by hand. Because finding eigenvalues, eigenvectors and row reduction is tedious, I gave in to the temptation of just writing the code which any highschool student can do. While the working Mathematica gave me a good coding skills, I can't help but feel I have some loose ends by relying on the computer too much. At times I think that doing the problems was mental hazing. I wasn't able to do all of them particularly the more difficult ones. The problems are divided into two parts: the first is the regular problems and the few hard ones. I didn't even touch the hard ones. I good feature of the chapters is at the end there are worked examples where you are given a problem and solve it before you look at the solution. Finally, Strang's lectures are available at opencourseware at MIT. I think they are also at Youtube. I look back at my self study now and regret not taking advantage of it

I purchased two copies of this book so I could teach my 17 year old homeschool senior Linear Algebra before she goes to college. The subject is by no means easy, yet Dr. Strang breaks it down, making it as simple as possible. Just in Chapter 1 (Introduction to Vectors), for instance, we spent three weeks. I learned more about vectors in three weeks than I did in four years of college. We're combining this text with the MIT lectures available on the internet and her progress is amazing. Whether you are taking Linear Algebra for the first time or if you need a refresher I highly recommend this book.

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.

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. I found the organization difficult: he would introduce certain ideas and topics too early. I found he rushed through certain sections I feel like certain chapters he could've demonstrated special cases or tricky problems. He emphasizes looking at the implications of the subject, which is my opinion is too much to ask for a beginner. This book is for people who are deep thinkers, who have great mathematical skill. For those spoiled by the minimalist, straight forward logic proof-like problem solving usually used in college calculus and algebra books, look somewhere else (if possible). I found the online MIT lectures and especially the online recitation with a little khan academy invaluable in learning the subject. With the exception of a few key chapters (intro to diff equations) the book was no help.

I bought this book because im taking the online Linear Algebra course on OCW MIT and this book is the required textbook for the course. In my opinion you have to struggle a bit to get the idea of what the text is trying to say,it helps very much if you watch the videos, but even still I think sometimes explanations are very vague. Most of the example problems are relatively easy, but most of the drill problems are very complicated and completely unrelated to the main idea of the chapter. I think many of the problems deviate you from the main idea, for example you may be trying to learn how to perfect gauss-jordan reduction, and instead you are encountered with problems like finding all the edges of a hypercube, now im not saying its not related to the topic at hand, but it deviates you from the main point you are trying to learn, so stick to the more familiar ones and the ones you think are more useful. After a while of reading the book, watching the online lessons and recitations, solving problems, etc.. I think I have learned quite a lot, but its more a combination of all those things rather than the book itself, if I had to rely solely on the book I think I would've looked for something else, professor Strang's lectures are good but he jumps back and forth from idea to idea sometimes without finishing the previous idea, which is confusing, and that is also reflected on this book. I find David Poole's Linear Algebra book a lot better, its easier to understand, its better written, almost the same topics are addressed but the problems are designed to futher enhance your habilities, plus it has a lot more real applications. Bottomline get this book if and only if you are planning on taking the MIT online course, otherwise look for something else (in fact even if you take the MIT course it wouldnt hurt to get this book plus David Poole's book so you can read both)

I've read many linear algebra books, and this was the best until now. It doesn't contain detailed proofs for all theorems (you can find hundreds of books which do that), but shows the roots of linear algebra, and leads the reader to a deep understanding, through lots of examples, and solved exercises. After one got a full picture, he/she can proceed to the detailed proofs of the theorems. In addition you can watch all linear algebra lectures of prof. Strang freely on Youtube, just search for "MIT Openopencourseware" or for "Gilbert Strang".

Strang is an amazing teacher. He turns linear algebra into an exciting subject. I studied this textbook by myself, together with the video material I found on MIT OCW Scholar. Strang writes the way he talks, which is good, because he talks to you like a real person. Just take a look at one of his videos and you'll know whether you like his style. Do not believe the reviewer who says that this book is "terrible for self-learners". There are enough worked examples and many exercises with solutions in the back.

if you're looking for an introduction to linear algebra GET THIS BOOK. it's very in depth and may go beyond your curriculum, but you will find everything you need in here explained with crystal clarity. i'm a second year student studying statistics and i've used many linear algebra textbooks and this is by far the best. it's also accompanied by lectures on the MIT youtube channel where Strang gives some of the most clear lectures i've ever seen. the book also has MATLAB instructions which i have yet to get into in my second linear algebra course.

分かりやすく、また問題も豊富なので順に解いていけば理解できるようになっています。英語も非常に容易なので洋書に取り組む第一歩としてもおすすめです。

This book is fantastic , I would recommend anyone studying or thinking of studying linear algebra to buy this . I would recommend anyone to buy any book written by Gilbert Strang.