Lectures on Linear Algebra (Dover Books on Mathematics) [Paperback]

I. M. Gel'fand (Author), Mathematics (Author)

Book Description

ISBN-10: 0486660826 | ISBN-13: 978-0486660820 | Publication Date: September 1, 1989

Prominent Russian mathematician's concise, well-written exposition considers: n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Editorial Reviews

Review

."..a wonderful reference for anyone interested in planning radio-based networks." ("Computing Reviews.com", May 2, 2007) --This text refers to the Hardcover edition.

Language Notes

Text: English (translation)
Original Language: Russian

Product Details

• Paperback: 185 pages
• Publisher: Dover Publications (September 1, 1989)
• Language: English
• ISBN-10: 0486660826
• ISBN-13: 978-0486660820
• Product Dimensions: 8.4 x 5.5 x 0.4 inches
• Shipping Weight: 4 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (6 customer reviews)
• Amazon Best Sellers Rank: #890,169 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

15 of 16 people found the following review helpful:

5.0 out of 5 stars Excellent and Compact book, December 10, 2005

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
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This review is from: Lectures on Linear Algebra (Dover Books on Mathematics) (Paperback)

The professor who recommended this book made the comment that every time you re-read it, you notice something else that you missed the last time you read it. This is absolutely true.

I must say, the first time I picked up this book, I did not like it. The notation was not what I was used to, and the book dives right in, assuming a lot of background (matrices, determinants, etc.) but covering material which many people find boring (bases, etc.). However, when you read deeper, there's a lot here. Once you get past the ugly notation, the proofs are extraordinarily clear. And in spite of the books small size, there is a remarkable amount of motivation and discussion.

Like the other reviewer said, this is not a book to learn linear algebra from for the first time: this is an advanced book that is useful for graduate students who have already had a linear algebra course and who want to learn more topics, or understand topics on a deeper level.

This is an excellent book; the bottom line is that it's so cheap that there's no excuse NOT to buy it.

17 of 20 people found the following review helpful:

3.0 out of 5 stars Good as a reference not for learning, February 27, 2003

By 

Alexander Vorobiev "A witty saying proves not... - See all my reviews
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This review is from: Lectures on Linear Algebra (Dover Books on Mathematics) (Paperback)

This is a good book if all you need is a condenced reference on theorems and proofs and it assumes that you go for practice (and instruction) elsewhere. If you are trying to actually learn linear algebra (especially on your own and especially if you want to learn how to solve practical problems) get one of Gilbert Strang's books and watch his videolectures at MIT web site. Another thing that I dislike about the Gelfand's book is that it puts too much emphasis on index notation - instead of matrix notation wich is natural for linear algebra, almost all formulas and theorems are presented at very low level using expressions consisting of variables with multiple indices. Naturally it gets very messy and hard to follow at times. This doesn't present any more information than equivalent matrix notation but introduces unnecceccary complexity and makes things that are really easy to understand very confusing.

2 of 2 people found the following review helpful:

5.0 out of 5 stars Very good textbook for the application-minded person, October 16, 2010

By 

J. R. G. Mendonca (SP, Brazil) - See all my reviews
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This review is from: Lectures on Linear Algebra (Dover Books on Mathematics) (Paperback)

I can only strongly recommend this somewhat forgotten textbook to anyone who needs a basic but otherwise thorough exposition to linear algebra. It conflates rigor, examples, and exercises very nicely, although in a very economic manner. Its coordinate-oriented presentation may not appeal to the mathematician in search of ultimate generality, but it is ideal for the physics and engineering-minded person. It is unfortunate that nowadays so many S&E students become first aquainted with rings of polynomials than with rotation matrices! Do not get me wrong, though: the book contains real math inside, but in the best Russian textbook presentation tradition.