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Linear Algebra (Dover Books on Mathematics)
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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.
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 This book may come across as a bit old-fashioned, and some might say the material is obsolete, but I believe that everything contained in the book is useful, if only to give the reader a deeper understanding of the why's and how's of linear algebra.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!
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 ›
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.
Most Recent Customer Reviews
Simple,useful tool for a student.Formally correct and elegant as to demonstrationsPublished 8 days ago by Cliente Amazon
This member of the series of math books from Moscow State University, by professor Georgi E. Shiloh, gives a birds eye view of how Linear Algebra is taught in Russia. Read morePublished 3 months ago by Herbert L Calhoun
As said in earlier reviews, this is not a beginners text. This is not written or translated in a format employed by other Linear Algebra texts or on line courses. Read morePublished 10 months ago by Bradford T. Taylor
I am trying to learn linear algebra on my own time in preparation for college. I bought this book because it was cheap and I have had good experiences with dover previously. Read morePublished 17 months ago by Daniel
This book is terrible. It is out dated, poorly presented, the symbols are too small to see, there is poor explanation. This book is bad all around. Read morePublished 21 months ago by Paul T. Cusack