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Title: Linear Algebra
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Manufacturer: Dover Publications
List Price: $16.95
Our Price: $9.64
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| Customer Reviews: |
| Linear Algebra by Dover Publications Not that good | | Ordinarily I would give this book three stars, but I feel the rave reviews must be offset further than that. The first chapter on determinants is very good, it gives you the why and the how of everything. Perhaps this is due to the somewhat concrete, computational nature of determinants, which favors Shilov's approach. Shilov retains this sort of computational orientation throughout the text, with very little attention paid to the visual/intuitive aspects of linear algebra. A particularly atrocious example of this is chapter 5 on coordinate transformations. He derives formulae for a multitude of different types of coordinate transformations without ever describing what the transformation accomplishes in intuitive terms. This can be troubling even for someone who already has a reasonable understanding of the subject, because it means that ultimately his presentation amounts to little more than a mere presentation of a lifeless formula, and you are left to determine for yourself what it amounts to. Indeed, all of the chapters, with the exception of the first, share in this general flavor. Computational in flavor, as opposed to conceptual or abstract, while at the same time weak in visual/intuitive content. To me this is not a winning combination, and has made for a rather miserable read. In all fairness, however, I should add that his coverage is pretty good, albeit a bit unorthodox as far as the order of presentation is concerned. You can learn linear algebra from this book, it just won't be that fun. | | Linear Algebra by Dover Publications a great classic treatment of a fundamental subject | 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. | | Linear Algebra by Dover Publications Not the best, but, then again, nothing is. | | I couldn't really find a truly good, comprehensive linear algebra textbook. This is one of the better ones. You don't even want to touch one of the worse ones. | | Linear Algebra by Dover Publications Outstanding Book | 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! | | Linear Algebra by Dover Publications Great book | | 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. | | Linear Algebra by Dover Publications Product Description | 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.
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