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Introduction to Linear Algebra, Third Edition | 
 enlarge | Author: Gilbert Strang
Publisher: Wellesley Cambridge Pr
Category: Book
List Price: $82.50
Buy New: $64.14
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Rating:  29 reviews
Sales Rank: 15618
Media: Hardcover
Edition: 3
Pages: 568
Number Of Items: 1
Shipping Weight (lbs): 2.6
Dimensions (in): 9.2 x 7.6 x 1.3
ISBN: 0961408898
Dewey Decimal Number: 512
EAN: 9780961408893
Publication Date: March 1, 2003
Shipping: Eligible for Super Saver Shipping
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Product Description
This informally written text provides students with a clear introduction into the subject of linear algebra. Topics covered include matrix multiplication, row reduction, matrix inverse, orthogonality and computation. The self-teaching book is loaded with examples and graphics and provides a wide array of probing problems, accompanying solutions, and a glossary. 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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| Customer Reviews: Read 24 more reviews...
 The engineer's classic. July 26, 2006
wiredweird (Earth, or somewhere nearby)
17 out of 17 found this review helpful
People say that mathematical truths never change, and that's true enough. New concepts, applications, and techniques keep emerging, though, so math teaching needs to keep up with the times. Strang has done an outstanding job of keeping this book current and relevant.
It's not a mathematician's math book - this is aimed at people who need results and needs computational techniques more than they need crystalline theorems. That's why it's so helpful to see applications like Markov models, Kirchoff's laws, and Google's analyses of the web. It's also helpful to see examples worked in Mathematica and MATLAB, the tools of choice for desktop exploration of numerical systems. It's startlingly easy to come up with a 100x100 system of equations, and just nuts to try to solve it by hand.
Strang assumes some amount of calculus in this book, something that other books on linear algebra sometimes skip. That raises the bar for the readership, but also opens up topics like change-of-basis in function space, including Fourier analysis. It also allows differential equations to be addressed as linear systems. Even without calculus, though, a reader is exposed to the singular value decompostion, QR and other matrix decompositions, and considerations in performing the computations. I found a few oddities, such as the description of a matrix's condition number. That has great physical meaning when it's taken as the ratio of the matrix's highest and lowest eigenvalues, but Strang gives a definition that I found less intuitive.
Such oddities are rare, though. Even though this book covers many topics, its emphasis is on clear and applicable presentation. I recommend this to anyone studying linear algebra or who, like me, has to brush up on basics not used in many years.
//wiredweird
Teach the subject to the non-math students February 25, 2004
bal gombak (Cambridge, MA USA)
31 out of 37 found this review helpful
Gilbert Strang is a very experienced teacher of Linear Algebra, and this book is written as a text based on his MIT linear algebra class. Math majors will not find the 'definition-proposition-lemma-theorem-proof-corollary' treatment here. Instead Strang, aware of the need to teach non-math majors the subject, explains linear algebra in a simple but effective way --examples, diagrams, motivations. This book is one of those with which you can skip class the whole semester and get good grades (but don't do it! get your education in the classroom).
A wonderful book May 24, 2006
Mr. D. Otgaar (Cape Town, South Africa)
21 out of 21 found this review helpful
As someone who already knows the basics of the subject, I guess I'm looking at things with the benefit of hindsight. However, I needed to shore up my own knowledge of Linear Algebra and thought I might as well turn to Strang for a refresher and a different approach.
The result is that I am truly pleased with this book. His writing is lively and engaging. Linear Algebra has a phenomenal tendency to get dry and Strang does an excellent job of turning the subject this way and that so that one can admire it from every angle. In particular, there are three major approaches in this book that make it stand out.
1. Strang places heavy emphasis on vectors, vector spaces and transformations. This is good preparation for future study in Linear Algebra. This will provide an intuitive understanding of linear operators on vector spaces later.
2. Another reviewer mentioned that the book utilises a discovery-based approach. While this might be a disadvantage when you're in a hurry, the approach prepares one well for learning more theoretically oriented subjects where self-guided discovery is imperative. In this sense, I think the discovery approach is far superior to others and prepares the reader well for future studies. The problems are really fun (although I personally think they are much too easy). Many of the questions require light-weight proofs without undue formalism (not really required at this level). These pseudo-proofs really do help build understanding of the subject. Maths-phobes will not even realise that they're fleshing out the subject themselves.
3. The didactic approach taken in the book is conversational and informal. When added to the freely available video lectures at the OCW site, given by Strang himself, you really have a perfect introduction to the subject of Linear Algebra. The lectures are superb and Strang is an excellent teacher. His enthusiasm and passion for the subject is obvious and infectious.
I really wish I had learned Linear Algebra from this book initially. The book does a good job of encouraging geometric intuition and visualisation. That said, I do not think the book is an ideal book for maths majors. The primary problems being too little exposure to abstraction and problems which are too easy. However, I do believe that the book can be used in conjunction with a more rigorous approach in cases where the latter gets just a touch too dry. There is time to develop the rigour in theoretical Algebra courses at a later stage, with the added benefit that the reader will have learned the experimental approach to learning taken in the book.
I suppose some will find Strang's excitement over Linear Algebra a bit of a pain, but personally I think this conveys the sheer joy of pursuing an intellectual endeavour. I've always bordered on disinterest with Linear Algebra and this has been very much dispelled. I like to be reminded why I chose to study mathematics in the first place sometimes. While I can see that this book isn't for everyone, I really enjoy it and recommend it highly.
A unique entry in math texts--it isn't dry! January 2, 2006
Jessica Lux (Rosamond, CA)
9 out of 11 found this review helpful
This is a pleasant surprise of a math text for higher education in that the prose isn't dry and the author fills the text with practical examples and explanations. How many times has the university math or engineering student read a text that derives one theorem and then expects the reader to apply it to a multitude of situations with no extra extrapolation by the author? In Strang's refreshing affront to modern university texts, he employs a conversational (and comfortable!) tone to draw the reader in to the subject of Linear Algebra. I've seen this billed as "Linear Algebra for the non-math major," but I reject that advertisement--every engineering and math student should get a nice change of pace with this text.
The text has the necessary solutions to selected (most) exercises, which make working through the problems much easier, since the student can get instant feedback about their solutions. Also, on a major plus side, this book is relatively compact and lightweight compared to other tomes of higher education.
Exactly what is needed November 4, 2003
G. Cantor (Mill Valley, CA USA)
28 out of 32 found this review helpful
Dr. Strang's book is, hands down, the best introductory Linear Algebra text on the planet. Other reviewers complain about the "discovery" approach and the conversational style; in my view, these are strengths not flaws.First of all, we have lost our way with modern mathematics texts by all but eliminating the idea of discovery. Nothing can strengthen the learning and understanding of mathematical material more than having to "find out for yourself" what is going on. Absent that process, one can only reach a superficial understanding of the topic at best. Second, it's refreshing to see a truly conversational approach. Once again, there are too many dry definition-theorem-proof texts out there ... they're maybe appropriate for a more advanced exposition, not for an introduction. In many ways I agree with Dr. Strang that we teach too much calculus and not enough linear algebra. The former has been the standard sequence for undergraduate mathematics for years; nifty stuff but seldom, if ever, seen outside the classroom. Linear algebra, on the other hand, is alive and well in industry and just may be the most useful set of mathematical tools available to the technical types. Everone studying or using linear algebra would find time spent with Dr. Strang's book an excellent time investment. And for those not liking discovery or conversation, maybe you should try a different course of study ... you've missed the boat on this one!!
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