Linear Algebra |
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| Title: | Linear Algebra |
| Author: | Georgi E. Shilov |
| Publisher: | Dover Publications |
| Type: | Book / Paperback |
| Publication Date: | 01 June, 1977 |
| ISBN / ISBN-13: | 048663518X / 9780486635187 |
| List Price: | $16.95 |
| You Save: | $5.42 |
| Amazon Price: | $11.53 |
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This book is also available, brand-new, from 3rd-party marketplace sellers at Amazon.com, from $10.00.
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Editorial Review / Publisher's Information:
Product Description
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; hints and answers.
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Customer Reviews:
• Slow Going (for Me Anyway)
04 March, 2009
Full disclosure: I'm not finished with this book yet. My last encounter with linear algebra was in 1978, so I expected some head-scratching. But it took me many hours just to get 25 pages into this book. Linear algebra is not Einstein science, so I was worried. I compared this book to my 30-year-old college textbook, and the college textbook wins. This book is lacking in examples. A theorem is presented, then proved, then given a reference number, and then pops up later by reference number, forcing use of many bookmarks.
On the positive side, the price is a bargain. And, the translation from the original Russian is absolutely invisible.
- Amazon Customer Review
• Excellent Linear Algebra Text
30 October, 2009
I needed to refresh my understanding of linear algebra and so I read Shilov.
I studied matrix algebra 40 years ago and I needed to refresh my algebra skills. This text was just exactly the review I needed.
- Amazon Customer Review
• Good Mix Of Theory And Computation
31 December, 2008
There are a lot of linear algebra-matrix theory books around, and for my next course I picked Shilov's book. (It is advanced undergraduate/beginning graduate level.) So what is special about this it?
It has a good mix of theory and computation. It has many exercises, and they help in the learning, I think, better than some of the books I looked at as well. Some of them have hints, and some answers, listed in the back. Processing matrices is a visual thing. Shilov's book includes lovely pictures of matrices, and their block components. This is a big help in teaching matrix products, inverses, determinants, diagonalizations, not to mention applications to geometry, conical sections, projective space, and tangent planes.
The beautiful pictures are many, are superb, are artistically done and include graphical illustrations, figures, surfaces and more. They may not be created with the latest software, and yet they are timeless, and better IMO than the glossy ones found in newer editions.
Another thing I like about Shilov's book is its use of multilinear algebra. It is motivated by differential geometry of course, but it is great for applications to for example invariant theory.
There is a number of great alternative choices, some priced in the $ 100 range; and yet I found that Shilov ($ 10) has an edge; even forgetting the price.
Sample of topics: Standard fare on linear algebra and matrices, systems of equations etc; vector spaces and their duals, inner product, linear transformations and their adjoints; canonical form, quadratic forms & extrema, unitary space, Jordan forms, and a nice selection of timeless applications. Review by Palle Jorgensen, December 2008.
- Amazon Customer Review
• Good Book, Great Price
26 January, 2009
This makes for a good second book on Linear Algebra. If you aren't familiar with some of the basic concepts of linear algebra such as determinants, eigenvalues, or matrices, this book probably isn't for you. You should also have some experience with a more proof-oriented approach to mathematics. If you do, you'll get a lot out of this book. The best part is, it's only $12. You won't find another linear algebra book this good for anywhere near that price.
- Amazon Customer Review
• Rigorous And Rewarding
15 February, 2009
Shilov's Linear Algebra is a great book for mathematicians wanting a detailed and rigorous exposition of the subject matter. All the standard topics in linear algebra are covered, such as: determinants, cofactors, minors, and more topics in matrix algebra; linear spaces; linear and bilinear operators and forms; quadratic forms; matrix representation of linear functions; eigenvectors and eigenvalues; Euclidean and Hermitian spaces; orthonormal bases; etc. Some more advanced topics are also touched upon; there are brief sections on tensors, multilinear forms, and spectra, jets and polynomials, but I wouldn't recommend this book to learn about these, as there are more complete treatments elsewhere. There are also two appendices, one on some basic representation theory, the other on category theory. Again, this is not the best book to learn about these topics, but it is interesting that they are included, perhaps to show some theoretical applications of linear algebra.
The proofs are detailed and precise, making the book great for self-study. A few of the proofs are actually quite original, which is impressive for such a well-worked subject. There are also large and comprehensive problem sets at the end of each chapter, with either full solutions or hints given in the back. This book is also good in that it is mostly self-contained, presupposing almost no prior knowledge of linear algebra or other fields of mathematics.
This would probably not be a good book for someone learning linear algebra for the very first time, or for someone looking for a quick-and-easy reference for formulas. Shilov takes the pure mathematician's approach of presenting everything with a high degree of generality, probably more than would be necessary for most undergraduate college classes in linear algebra or for engineers and computer programmers. But if you're a mathematician looking for a complete and self-contained account of this fundamental subject, or just someone who enjoys the rigor and beauty of pure mathematics, this is the book for you.
- Amazon Customer Review
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