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'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".

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。

A must read for everyone who has interest in math and math applications. Great writing , self-explanatory, with hundreds of examples and exercises. Solutions to exercises are provided in the 18.06 course of MIT website.

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.