Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Then you can start reading Kindle books on your smartphone, tablet, or computer - no Kindle device required.

  • Apple
  • Android
  • Windows Phone
  • Android

To get the free app, enter your email address or mobile phone number.

Linear Algebra (Dover Books on Mathematics)

4.1 out of 5 stars 43 customer reviews
ISBN-13: 978-0486635187
ISBN-10: 048663518X
Why is ISBN important?
ISBN
This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The 13-digit and 10-digit formats both work.
Scan an ISBN with your phone
Use the Amazon App to scan ISBNs and compare prices.
Have one to sell? Sell on Amazon
Buy used On clicking this link, a new layer will be open
$9.95 On clicking this link, a new layer will be open
Buy new On clicking this link, a new layer will be open
$13.85 On clicking this link, a new layer will be open
More Buying Choices
41 New from $5.46 53 Used from $4.99
Free Two-Day Shipping for College Students with Amazon Student Free%20Two-Day%20Shipping%20for%20College%20Students%20with%20Amazon%20Student


2016 Book Awards
Browse award-winning titles. See all 2016 winners
$13.85 FREE Shipping on orders with at least $25 of books. In Stock. Ships from and sold by Amazon.com. Gift-wrap available.
click to open popover

Frequently Bought Together

  • Linear Algebra (Dover Books on Mathematics)
  • +
  • Ordinary Differential Equations (Dover Books on Mathematics)
  • +
  • Fourier Series (Dover Books on Mathematics)
Total price: $42.67
Buy the selected items together

Editorial Reviews

Language Notes

Text: English, Russian (translation)
NO_CONTENT_IN_FEATURE


Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 400 pages
  • Publisher: Dover Publications (June 1, 1977)
  • Language: English
  • ISBN-10: 048663518X
  • ISBN-13: 978-0486635187
  • Product Dimensions: 5.6 x 0.8 x 8.4 inches
  • Shipping Weight: 11.2 ounces (View shipping rates and policies)
  • Average Customer Review: 4.1 out of 5 stars  See all reviews (43 customer reviews)
  • Amazon Best Sellers Rank: #36,360 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

Format: Paperback
This is a solid book, but requires a degree of mathematical maturity. Like many of the Dover publications of translated Russian mathematical texts, the book is clearly written, with good proofs that are easy to follow, lots of useful examples, and solutions to problems are given at the end of the book.

Readers should note that the author is a noted Russian mathematician, a former professor of mathematics at Moscow University, one of great centres of mathematical research and teaching in the world. Shilov collaborated with many important mathematicians such as Kolmogorov and Gelfand. If you have read any of Kolmogorov or Gelfand's excellent Dover books, then the style of this book is very similar to those.
Comment 139 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
I find it ironic that my two favourite Linear Algebra texts are this book and the Axler, for they are exact opposites: Axler shuns determinants, and Shilov starts with them and builds much of his theory off them. However, there is no book I have found that has such a deep and clear exposition of determinants. The first chapter alone makes this book worth buying.

However, there's an incredible amount of material in this book, and the later chapters are just as valuable. This is a dense book, but it is fairly easy to read once you get used to the style. I would recommend it to anyone learning linear algebra for the first time, as well as to people who want a deeper understanding or a different perspective.

Like I said before, this book is particularly useful when combined with a complementary text such as Axler, which provides a completely different approach to the subject. This book may come across as a bit old-fashioned, and some might say the material is obsolete, but I believe that everything contained in the book is useful, if only to give the reader a deeper understanding of the why's and how's of linear algebra. And plus: you can't complain about the price!
5 Comments 78 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
If you are trying to learn linear algebra for the first time, avoid this book. You will be better served by Schaum's Outline of Linear Algebra Fourth Edition (Schaum's Outline Series). However, if you already have a working knowledge of the basics, have realized the central importance of this subject, and are trying to reach a deeper understanding of it, this is the book for you.

Here is a brief rundown of the contents:

Chapter 1 is on the theory of determinants. It is excellent and forms the basis of the entire book. It also immediately shows the sole focus of this book: finite dimensional linear algebra.

Chapter 2 is on linear spaces. Here as in his other books, Shilov moves to the abstract very early in his treatment. Anyone reading this book should be prepared by at least having the background of Schaum's Outline of Set Theory and Related Topics. It is noteworthy that this book does not even admit the existence of infinite dimensional vector spaces. Indeed, a basis for a vector space must be finite by definition. This is quite nonstandard, but again shows the focus: finite dimensional linear algebra.

Chapter 3 treats systems of linear equations. This chapter moves us back to the concrete, but again this book is only for readers with a firm grasp of the basics. Gaussian elimination is never even mentioned, but Cramer's rule is discussed in detail and used frequently for the rest of the book as a powerful theoretical tool.
Read more ›
2 Comments 42 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback
Like most of the Dover books, this is a reprint of a classic text. This means that there is not a lot of hand-holding, only solid, clearly explained mathematics for those who have the motivation and want to put in the effort - not like our friend rururu who learns his math from Schaum's outlines. Shilov is one of the great mathematicians of the 20th century and so his proofs are well done and are very helpful for anyone wanting to have a real understanding of linear algebra and the follow on courses of ordinary and partial differential equations.
2 Comments 35 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse
Format: Paperback Verified Purchase
5 stars for the author, but regrettably only one star for the translator. Dr. Richard Silverman should stay well within his expertise which is mathematical translation. Please do not second guess the thinking behind the Russian genius. Dr. Silverman, in the process of freely editing, transformed a masterpiece from a mathematical authority into a monster's piece. There are numerous typos and simple algebra, and sometimes conceptual errors to make the book legitimate for learning mathematics. For example, in section 6.1, the lengthy construction of the "Canonical Form of the Matrix of a Nilpotent Operator", The translator completely mixed up the construction of space (H sub r) making it almost impossible to follow. It is not a typo error as claimed by the translator.

However, regarding to the real content of the book,
it is a masterpiece from a mathematical genius. Brilliance mathematical expositions and beautiful proofs. The expositions are coherent and rigorous. And though, it would have been very readable if the mistakes were corrected.
2 Comments 28 people found this helpful. Was this review helpful to you? Yes No Sending feedback...
Thank you for your feedback.
Sorry, we failed to record your vote. Please try again
Report abuse

Most Recent Customer Reviews

Set up an Amazon Giveaway

Linear Algebra (Dover Books on Mathematics)
Amazon Giveaway allows you to run promotional giveaways in order to create buzz, reward your audience, and attract new followers and customers. Learn more
This item: Linear Algebra (Dover Books on Mathematics)