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A (Terse) Introduction to Linear Algebra (Student Mathematical Library) Paperback – December 19, 2007

ISBN-13: 978-0821844199 ISBN-10: 0821844199

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Product Details

  • Series: Student Mathematical Library (Book 44)
  • Paperback: 215 pages
  • Publisher: American Mathematical Society (December 19, 2007)
  • Language: English
  • ISBN-10: 0821844199
  • ISBN-13: 978-0821844199
  • Product Dimensions: 5.5 x 8.5 inches
  • Shipping Weight: 1 pounds (View shipping rates and policies)
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (4 customer reviews)
  • Amazon Best Sellers Rank: #452,804 in Books (See Top 100 in Books)

Editorial Reviews


"This little book is a pleasure to read... In short, there are many who can get a substantial amount out of this little book, and I am definitely glad to have read it..." ---- MAA Reviews

"The book is written in an elegant, condensed way. It contains many exercises, mostly of theoretical character. The main advantage (in particular for teachers and talented students) is that basic ideas are carefully isolated and presented in a simple, minimal and understandable way." ---- European Mathematical Society Newsletter

"...embodies a beautiful, concise and precise treatment of the subject as a part of general algebra. ... Students of pure mathematics will cherish this book as a wonderful, direct path through linear algebra in a general algebraic setting." ---- Zentralblatt MATH

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6 of 6 people found the following review helpful By Georg Cantor on November 12, 2010
Format: Paperback
This text is written for advanced undergraduates (and beginning graduates as well). It comprehensively covers the theory in an abstract setting. Being around 200 pages, it's presented in an elegant, modern, streamlined, and concise fashion. It leaves the reader plenty of things to fill in, as well as a nice selection of good exercises. I bought this book on an impulse, just to have it in my library (already being well-versed in the subject). It would have been very nice to have learned from this book.

Comparing/Contrasting with other noteworthy Linear Algebra texts:
(1) Serge Lang - Linear Algebra; I learned from this book. Though Lang has written a bad book on just about every subject in mathematics, his Linear Algebra book is lovely, and comparable to this book. The main difference is that most of Lang's exercises have an "Algebra" flavor, in that they mostly require you to exploit the group structure of vector spaces; Katznelson's book (the book I'm reviewing) seems to take a more unified approach with its exercises.
(2) Georgi Shilov - Linear Algebra; it's a translation of an older Russian book. The notation is old/annoying, and (as is true for most translations of Russian books) the language/logic can be contorted and inefficient, though the theory is covered in a very classical way.
(3) Paul Halmos - Finite Dimensional Vector Spaces; it's another good book, though a bit out-dated, wordy, and geared with a more "Analytic" flavor.
(4) Sheldon Axler - Linear Algebra Done Right; this is another modern book. It's my favorite, behind the Lang and Katznelson (this) books. It seems to be a bit less abstract and down-to-earth, but nevertheless effective.

In summary, among other noteworthy Linear Algebra texts, I feel that this book is the best because of its broad coverage of the theory, concise exposition, and its modern and unified approach. So, in my opinion, for students of pure math, this is THE book to have for Linear Algebra.
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4 of 4 people found the following review helpful By Anonymous on December 9, 2009
Format: Paperback
This is a very nice little book on linear algebra. As the title says, the text is (very) concise. The main part of the book is covered in only about 160 pages with a large typeset. This has been achieved by short and elegant proofs and by leaving much of the work to the student. In addition, routine numerical examples are omitted. Quite a few proofs have been left as exercises and as it's remarked in the preface, some proofs are not complete to every detail and few are actually more like detailed lists of hints. Because of this, the book requires, and more importantly, exercises mathematical maturity. In my university it was offered as an advanced course for mathematicians but in Stanford, where the book comes from, the course is apparently aimed for second year students or so.

The text starts from the very basics and requires no prior knowledge on anything but an ability to read mathematical text. It certainly helps if you've taken a prior (numerical) introduction course to linear algebra. Because of the quick pace, theory goes surprisingly far I think (see table of contents from the book preview). There has also been room for additional topics for the interested. The presentation in the book is great and the text flows well. The chapters are divided into subchapters each of which has at maximum only one theorem, proposition, corollary and lemma, so that references are easy to follow. Proofs are short, intuitive and easy to remember once you get them.

The exercises are well chosen and certainly solvable even though the book has no solutions to them. There are practically no numerical examples or exercises, only proofs. Doing some of the exercises is an important part of studying the book properly.
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3 of 3 people found the following review helpful By Angad Kamat on September 29, 2008
Format: Paperback
I read a bit of this book to understand and refresh basic concepts of linear algebra. Being a Computer Science major, I did not need the details of linear algebra, and this reading was sufficient for a course on quantum algorithms. The contents are accessible to any non-mathematical majors with basic high-school level math. The book is perfect for CS/EE grad students who might need some linear algebra knowledge for topics like coding theory. Would highly recommend to anyone as a quick introduction/reference.
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...then this is your kind of book. Personally, I love it. A lot of my friends hate it. It's incredibly dense. So much so that many of the proofs are only outlined, leaving the reader to fill in the details. By doing so, this book has managed to engage me in reading it and keep me focused better than any other math book has. Unpacking each theorem definition-by-definition keeps me versed on all the definitions and other theorems I need to know. It's self-reinforcing. I wouldn't recommend it if you're not adept at parsing thick blocks of jargon and symbols. Definitely keep a supplementary text handy (like Wikipedia or Schaum's Outlines).
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