Linear Algebra (Dover Books on Mathematics) [Paperback]

Mathematics (Author)

Book Description

Publication Date: June 1, 1977 | ISBN-10: 048663518X | ISBN-13: 978-0486635187

Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.

Editorial Reviews

Language Notes

Text: English, Russian (translation)

Product Details

• Paperback: 387 pages
• Publisher: Dover Publications (June 1, 1977)
• Language: English
• ISBN-10: 048663518X
• ISBN-13: 978-0486635187
• Product Dimensions: 8.4 x 5.6 x 0.8 inches
• Shipping Weight: 13.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (26 customer reviews)
• Amazon Best Sellers Rank: #17,161 in Books (See Top 100 in Books)
  • #1 in Books > Education & Reference > Foreign Language Nonfiction > Russian

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Customer Reviews

Most Helpful Customer Reviews

92 of 95 people found the following review helpful:

5.0 out of 5 stars Excellent Linear Algebra Text, October 5, 2002

By 

S. Murphy (Oxford) - See all my reviews

This review is from: Linear Algebra (Dover Books on Mathematics) (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.

49 of 49 people found the following review helpful:

5.0 out of 5 stars Outstanding Book, December 10, 2005

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
(REAL NAME)   

This review is from: Linear Algebra (Dover Books on Mathematics) (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!

21 of 21 people found the following review helpful:

5.0 out of 5 stars Excellent Presentation of Linear Algebra, May 21, 2003

By 

Charles Saunders (Tallahassee, FL United States) - See all my reviews

This review is from: Linear Algebra (Dover Books on Mathematics) (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.