Linear Algebra (Undergraduate Texts in Mathematics) (Hardcover)

by Serge Lang (Author) "As usual, a collection of objects will be called a set..." (more)
Key Phrases: definite hermitian product, complex unitary matrix, symmetric linear map (more...)

Editorial Reviews

Review
"The present textbook is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of finite-dimensional vector spaces and proceeds to explain the structure theorems for linear maps, including eigenvectors and eigenvalues, quadratic and Hermitian forms, diagonalization of symmetric, Hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. It also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants, and linear maps. In this third edition, many parts of the book have been rewritten and reorganized, and new exercises have been added." (S. Lajos, Mathematical Reviews)

Product Description
"Linear Algebra" is intended for a one-term course at the junior or senior level. It begins with an exposition of the basic theory of vector spaces and proceeds to explain the fundamental structure theorem for linear maps, including eigenvectors and eigenvalues, quadratic and hermitian forms, diagnolization of symmetric, hermitian, and unitary linear maps and matrices, triangulation, and Jordan canonical form. The book also includes a useful chapter on convex sets and the finite-dimensional Krein-Milman theorem. The presentation is aimed at the student who has already had some exposure to the elementary theory of matrices, determinants and linear maps. However the book is logically self-contained. In this new edition, many parts of the book have been rewritten and reorganized, and new exercises have been added.

Product Details

• Hardcover: 296 pages
• Publisher: Springer; 3rd edition (March 9, 2004)
• Language: English
• ISBN-10: 0387964126
• ISBN-13: 978-0387964126
• Product Dimensions: 9.3 x 6.3 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars See all reviews (6 customer reviews)
• Amazon.com Sales Rank: #347,103 in Books (See Bestsellers in Books)

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Customer Reviews

Most Helpful Customer Reviews

18 of 22 people found the following review helpful:

5.0 out of 5 stars A very concise and rigorous book, April 26, 2000

By A Customer

It is the rare sort of book that makes an excellent introduction for the student and useful reference for the graduate, and that is why I recommend this book unreservedly. Its conciseness may leave some students adrift, but I think it serves to enhance the book's structural coherence. And while the given proofs are usually terse, I think that makes the book a wonderful way to measure one's prepardness for upper level studies. Linear algebra is the ideal subject with which to familiarize students with rigorous proof techniques because it has so many easily visualized yet useful examples. If one cannot understand Lang's proofs here, one is probably not ready to tackle an upper level course in, say, algebra or topology. This book therefore serves as a proving grounds, so to speak (and excuse the pun!), for one's mathematical ability. Survive the test and you'll probably do well in your upper level studies, otherwise you should practice some more and try again.

13 of 16 people found the following review helpful:

5.0 out of 5 stars Solid piece of work, October 26, 2004

By	J. C. Verheul - See all my reviews (REAL NAME)

This review is from: Linear Algebra (Undergraduate Texts in Mathematics) (Hardcover)

Like in other math books by Lang, the theory of Linear Algebra is presented in an axiomatic way, the best way of presenting since The Elements of Euclid. The way in which the theory is presented adds to the beauty. I have read this book as a refresher for Linear Algebra, about 20 years after the completion of a master's degree in an exact science. For me the level was perfect. If you have no experience with Linear Algebra beyond high school, you must first read "Introduction to Linear Algebra" by Lang or some other introductory course. The book under review does not talk about basics like Gauss-elimination. I have seen remarkably few typos. Some cross-references to theorems in other chapters were wrong, though. In all: a very good book and well worth the money.

3 of 3 people found the following review helpful:

4.0 out of 5 stars Difficult for undergrads, August 10, 2006

By	T. Morrison "math teacher" (baltimore) - See all my reviews (REAL NAME)

I think the term "undergraduate" is a bit misleading. I think you would have had to have at least one course in linear algebra and abtract algebra to truly appreciate this book. I read it over a summer (as a master's student who lacked any coursework in linear algebra) - kind of as an independent project, and I found it to be very easy to understand. Then again, I had just taken abstract algebra. There were a couple parts that I found challenging though. I love it when he says that the proof or rest of the proof is "trivial" and unnecessary to write. I have heard he does this in many of his books. Overall great book if you have some background.