Linear Algebra

Rating:
Summary: good, but not always a fun to read ...
Review: I only read the first 60 pages and then I stopped reading the book. Reason : while the book contains some interesting topics and certainly goes very deep and treats linear algebra in an abstract and rigorous framework, I had the impression that the proofs were not always the shortest and most elegant ones. Also, linear algebra at this level is not an easy topic, so Dover books, well known for their high quality on the contents, are not always the ideal books to learn from since the editor tries to put as many text on one page as possible in order to keep the price low. This makes it hard to read and also to make annotations.
For learning the basic principles of abstract algebra, I prefer the book : Linear Algebra: An Introduction to Abstract Mathematics by Robert J. Valenza. Valenza 's book succeeds in explaining the same basic ideas in a rigorous way but by choosing much more elegant proofs. This results in less pages to read while having a better understanding of abstract algebra.

Rating:
Summary: Excellent Linear Algebra Text
Review: I would advise readers to ignore the mindless comments
made by one of the reviewers of this book.

Books on linear algebra don't come better than this. Sure, it is not for dummies like 'rururu', but for the mathematically mature. It is very concise, so you must be prepared to spend a little effort if you don't understand something immediately. I found the book very 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 very important 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.

Rating:
Summary: Don't buy this book-waste of money
Review: If you are new to linear algebra, (even if you took introductory course), don't buy this. All those who took Linear Algebra course using this book got to hate the subject. Cheap for the content? Yes, of course. Because the content is not good. Not constructed well. I'm relearning it using Schaum's Outline, which is good and now I understand what was written in this awful book.

Rating:
Summary: Excellent book
Review: 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.

Rating:
Summary: Excellent Presentation of Linear Algebra
Review: 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.

Rating:
Summary: Excellent introduction to Linear Algebra
Review: This is an Excellent book, and also [a] very [good value] for their quality (I will never understand the reason for which other books, bad some of them, reach prices so high presenting topics that are treated by other books so [very good value] as this, and that they present the topics in excellent form). Comparing it with the book of Mirsky I encounter substantial differences, although the content characteristic of the linear algebra doesn't change. It treats the determinant defining them in a single formula and once and for all. Mirsky makes it defining the whole content of the theory of Silvester, more enriched, more substantial. Shilov extends the theory of the determinant along the book, while Mirsky makes it in a single chapter dedicated to its study. Mirsky conserves along the whole book, a classic presentation of the lineal algebra, while Shilov tries to enrich the topic introducing elements of modern algrebra. Mirsky has more exercises at the end of each chapter and they don't have answer, Shilov includes less, but it has answers to the exercises at the end of his book. Considering Mirsky my favorite one, I give a very special place to Shilov since he gives you a wider panorama and you terminate locating the lineal Algebra in a wider context inside the mathematics (definition of Algebras and a very good introduction to the algebra of the polinomiales, introduction to the tensorial algebra etc). This book is for an intermediate level, for undergraduates, and I recommend it to anyone that wants to study the linear algebra having the security that the concepts will be very clear. Their reading is easy to continue and it is a good introduction to the abstract algebra.

Rating:
Summary: Excellent book
Review: This is very complete and clear book . Excellent for applications. Treats topics usually omited in most linear algebra books . Could be used as reference .

Rating:
Summary: One of the Finest Texts on the Subject
Review: You can't get much better than Shilov when it comes to elegance of presentation. And the material here is fairly comprehensive, running smoothly from elementary topics to advanced ones. Although I will not recommend this text to beginning readers on the subject, I will recommend it to most others as an essential, useful, and very readable work.