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Linear Algebra (Undergraduate Texts in Mathematics) Paperback – 4 Oct 2013

4.0 out of 5 stars 10 customer reviews

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Product details

  • Paperback: 308 pages
  • Publisher: Springer; Softcover of Or edition (4 Oct. 2013)
  • Language: English
  • ISBN-10: 1441930817
  • ISBN-13: 978-1441930811
  • Product Dimensions: 15.5 x 1.8 x 23.5 cm
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (10 customer reviews)
  • Amazon Bestsellers Rank: 549,535 in Books (See Top 100 in Books)
  • See Complete Table of Contents

Product Description

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) 


Customer Reviews

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Top Customer Reviews

By A Customer on 29 April 1999
Format: Hardcover
I hope that in the coming reprint the author would take care to correct the numerous typos and errors in the 3rd edition. Though books are seldom free from mistakes, those in this book are particularly frustrating and confusing. The author did a lot of rearrangements from the 2nd to the 3rd edition, but many self-references in the book are not updated, and I could never figure out where the author refers to at some places.
Otherwise, I agree with the general opinion that this book is good but often too terse.
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Format: Hardcover
I sometimes joke that "mathematical maturity" is the ability to understand poor exposition. Lang's proofs are often too terse, and even experienced readers will sometimes have to work hard to fill in all the gaps. For this reason this book is not the best choice for most beginning graduate students. Nevertheless, time and time again in my study of algebraic number theory and algebraic geometry, when there has been some nugget of algebra that I had forgotten or never learned, I have found it in Lang and not in other standard texts. So for me, this book is an indispensable reference. Lang also has a knack for giving insightful summaries of advanced topics. Most other authors will at most mention an advanced topic without really telling you anything about it, but Lang actually gives useful introductions to a large number of topics of current research interest.
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Format: Paperback Verified Purchase
I was required to buy this book as part of my Undergraduate studies in Mathematics. The book does what it says on the tin. My overall feeling is that the book is fine, but a major fault is that there are no answers in the books, and so have no idea whether or not any answers are correct. There is a separate answer book available, but it is very expensive.
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Format: Hardcover
An excellent book, he takes beginners right up to advanced level. Very useful when taking an advanced course in linear algebra, if you haven't really broached the topic before. Far too expensive but I wouldn't let that put you off. There aren't enough worked examples, but if you buy this in conjunction with perhaps "Linear Algebra" by Seymour Lipschutz in the Shaum's outlines series, you will be fine.
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Format: Hardcover
Difficult to agree with my learned friend from Jackson,Mississippi that the chapters on groups and rings were boring. I must congratulate him on finishing the book in one week. More seriously, the book provides enough coverage of commutative algebra,Galois theory and homological algebra as to enable one to tackle the books by Eisenbud and Hartshorne on commutative algebra and algebraic geometry respectively.There are rival treatments by Cohn and Jacobsen but Lang beats them for conciseness.Lang is notorious for errors and omissions in his books and so one would expect a reader to have considerable 'maturity', i.e. the ability to correct proofs or fill in missing details.
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