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Linear Algebra 4th Edition Mass Market Paperback – November 21, 2002

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Product Details

  • Mass Market Paperback: 601 pages
  • Publisher: Prentice Hall India; 4th edition (November 21, 2002)
  • Language: English
  • ASIN: B003YNXP7U
  • Product Dimensions: 6.8 x 4.2 x 0.9 inches
  • Shipping Weight: 6.4 ounces
  • Average Customer Review: 3.9 out of 5 stars  See all reviews (60 customer reviews)
  • Amazon Best Sellers Rank: #186,525 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

32 of 33 people found the following review helpful By Kindle Customer on January 15, 2008
Format: Hardcover
A few introductory comments are in order: (1) This is *not* intended to be a first look at the subject of linear algebra, at least from the "computational side". (2) This is an undergraduate level text, though typically students will not encounter this material before their junior or senior years. (3) There is some overlap with a graduate level course in linear algebra, though this book is not comprehensive enough for a course at that level.

Ok, now that we've gotten that out of the way...

We used this as the primary textbook as a cross-listed advanced undergraduate/beginning graduate course I took in linear algebra. I had to supplement this book with outside reading/assignments to fulfill the balance of the course requirements. Contrary to what you might expect, you do not need an "introductory linear algebra course" (read that as "linear algebra for engineers") to successfully navigate this book. Actually, much (not all) of the material covered in this book should be discussed in any decent undergraduate course in ordinary differential equations (Boyce & DiPrima's ODE text makes a decent reference).

Here, you'll find that the emphasis is on learning the theoretical side of linear algebra. While there is a chapter (Chapter 3) on basic matrix algebra (wholly unnecessary in my opinion), the main use of matrices here is to express linear operators in a form more suited for computations, e.g., the determination of eigenvalues and eigenvectors. Right away, in Chapter 1, vector spaces are introduced and many familiar (some unfamiliar) examples are given. Just as in an abstract algebra course, you define a list of axioms for vector spaces (later, inner product spaces) and see what you can do with them...quite a lot, as it turns out!
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10 of 11 people found the following review helpful By khalee_daal on November 2, 2004
Format: Hardcover
For reference, I have done only a few of the problems and read no other books on Linear Algebra.

That aside, I can still attest that this is a good book. The proofs throughout are short, straightforward, and remarkably free of even trivial errors. The organization is sensible (at least from a theoretical perspective), and any definitions are generally introduced when the motivation has been established. The book is best geared for a math major, but I think the clarity is good enough to make it suitable for physics and engineering majors as well. To keep the book lively there are some well-developed examples in linear diffeq, economics, and einstein's relativity among others. These extra sections can ofcourse be skipped without loss of continuity. As per the problems, they are mostly of a trivial nature (dealing with concrete numbers) with a couple of intermediate proofs towards the end of each section.

My only gripe is that the authors take little initiative to ascribe geometric interpretations to results whenever possible; especially in the chapter on inner products. Frankly, it's easier to remember pictures then verbose thereoms.

If you do plan to read the book, I would recommend two semesters of calculus and possibly a preliminary course in abstract mathematics (sets and proofs).
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10 of 11 people found the following review helpful By math student on February 5, 2006
Format: Hardcover
This book blew me away! it's just great, it really explains everything (also an axiomatic approach of determinants which is very important to gain a thorough understanding of what determinants actually mean and which will help you when you are going to study multilinear algebra, exterior algebras in abstract algebra etc), the book gives you a good insight in the stucture of linear operators on a finite-dimensional vector space and provides lots of examples and useful applications (e.g. in economics and physics). There was a comment of one customer which criticized the fact that the theory doesn't offer an explanation of quotient spaces, this is true but in fact this is not important in the area of linear algebra, quotient structures should be studied in abstract algebra, when more algebraic structure has been developed so that one can really understand what quotients of algebraic structures are about. So the book is great, but I would recommend some knowledge about polynomials, fields, algebraic closure, vector space before starting to read this one.
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6 of 6 people found the following review helpful By Daniel G. Nolan on October 2, 2007
Format: Hardcover
I used the 3rd Ed. in UC Berkeley's MATH 110: Linear Algebra, then used the 4th while grading homework for the same class the next year. I think the book is fairly comprehensive (though by itself not enough to prepare one for grad school), and very well-written. The exercises at the end of each section span a wide range of difficulty. The book is self-contained, except for a few basic results from the calculus (one has to know the linearity properties of derivatives and definite integrals, i.e. derivative of linear combination is linear combination of derivatives and similarly for integrals), yet does sort of assume prior knowledge of linear algebra. At UC Berkeley students have already taken MATH 54: Linear Algebra & Differential Equations, which includes a brief treatment of vector spaces, linear transformations, eigenvalues, etc. I wouldn't say this book is "not for the faint of heart," as some reviewers put it. I think it's ideally suited--essential, in fact--for entering juniors majoring in the any of the mathematical sciences. If this book is your first exposure to linear algebra, then I highly, HIGHLY recommend chapters 12 and 13 of Calculus, Vol. 1: One-Variable Calculus with an Introduction to Linear Algebra (Second Edition), and chapters 1-5 of Calculus, Vol. 2: Multi-Variable Calculus and Linear Algebra with Applications.
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