Customer Reviews:
Showing reviews 6-10 of 13
 Great book September 16, 2005
R. Rathje (Seattle, WA USA)
7 out of 7 found this review helpful
This book has several good points. First, it is extremely affordable. Second, it covers all the typical topics in a typical undergraduate linear algebra course within the first 4 chapters or so. This makes it a great reference. I bought it as a supplement to my old linear algebra textbook, and it is great for that purpose. In addition, it continues on to more advanced topics which may not be covered at the undergraduate level; for example, the heavy emphasis on determinants and the more rigorous treatment of spaces, leading to affine spaces. I also have Shilov's book on real analysis, so I like the concise yet thorough manner of the author.
a great classic treatment of a fundamental subject March 2, 2008
mathwonk
1 out of 1 found this review helpful
I am choosing this book for my course on advanced linear algebra. This means nowadays a beginning course that covers all the bases, but that includes also some theory and proofs, and continues to the jordan form and spectral theorems.
I considered Axler, Lang, Hoffman Kunze, Halmos, and notes by Sharipov on the internet.
All these have their good points, but Shilov has it all: superbly clear explanations and proofs, examples and exercises, complete coverage of the important canonical forms, and a great elementary treatment of determinants, as well as tremendous attention to pedagogy.
E.g. like Halmos, Sharipov and some others, Shilov discusses nilpotent transformations separately and in detail, before doing jordan forms. since the idea of a jordan form is that every map is the direct sum of an invertible one and a nilpotent one, you would think it would make sense to discuss these types separately, but many books just cram the jordan form into one explanation with no discussion of nilpotent operators first.
finally, as a dover book, it is a terrific bargain. Friedberg Insel and Spence is a nice book, and Hoffman Kunze is also a classic, but those cost 10 times as much for about the same quality. I have reached the point in life where I will no longer assign a book that the publisher charges $135 for when there is a $15 book out there just as good or better.
Strangely however, not one student has ever expressed gratitude for this practice of mine in a class evaluation, but i suspect they appreciate it anyway, (or maybe Daddy is buying the books).
Edit: Having found cheap used copies of earlier editions of Friedberg et al..., I have relented and am using it also in my course. In general the earlier editions are better anyway. Some people have convinced me too that as clear as Shilov seems to me, it may be hard for some students to read.
Excellent book May 8, 2004
7 out of 10 found this review helpful
This is very complete and clear book . Excellent for applications. Treats topics usually omited in most linear algebra books . Could be used as reference .
One of the best books July 19, 2005
Dwija (co usa)
8 out of 11 found this review helpful
I am a graduate student and wanted to learn linear algebra for fun. This book provided me with one of the best coverage of the subject. It is supposed to be meant for upper level undergraduate courses or first year graduate studies .It is meant primarily for mathmatics graduates it starts right from basics and the proofs given are most succint and to the point. People who want to intutively learn the subject I would refer then to the book linear algebra and its applications.
all and all one of the best texts on the subject and compared to other books it gives more than other books with high price tags
Nitish
 good, but not always a fun to read ... August 17, 2003
20 out of 28 found this review helpful
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.
|
