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Matrices and Linear Algebra (Dover Books on Mathematics) [Paperback]

Hans Schneider , George Phillip Barker , Mathematics
3.6 out of 5 stars  See all reviews (14 customer reviews)

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Book Description

June 1, 1989 0486660141 978-0486660141 2

Linear algebra is one of the central disciplines in mathematics. A student of pure mathematics must know linear algebra if he is to continue with modern algebra or functional analysis. Much of the mathematics now taught to engineers and physicists requires it.
This well-known and highly regarded text makes the subject accessible to undergraduates with little mathematical experience. Written mainly for students in physics, engineering, economics, and other fields outside mathematics, the book gives the theory of matrices and applications to systems of linear equations, as well as many related topics such as determinants, eigenvalues, and differential equations.
Table of Contents:
l. The Algebra of Matrices
2. Linear Equations
3. Vector Spaces
4. Determinants
5. Linear Transformations
6. Eigenvalues and Eigenvectors
7. Inner Product Spaces
8. Applications to Differential Equations
For the second edition, the authors added several exercises in each chapter and a brand new section in Chapter 7. The exercises, which are both true-false and multiple-choice, will enable the student to test his grasp of the definitions and theorems in the chapter. The new section in Chapter 7 illustrates the geometric content of Sylvester's Theorem by means of conic sections and quadric surfaces. 6 line drawings. lndex. Two prefaces. Answer section.

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Product Details

  • Series: Dover Books on Mathematics
  • Paperback: 432 pages
  • Publisher: Dover Publications; 2 edition (June 1, 1989)
  • Language: English
  • ISBN-10: 0486660141
  • ISBN-13: 978-0486660141
  • Product Dimensions: 8.3 x 5.5 x 0.8 inches
  • Shipping Weight: 14.4 ounces (View shipping rates and policies)
  • Average Customer Review: 3.6 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Best Sellers Rank: #893,254 in Books (See Top 100 in Books)

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Customer Reviews

3.6 out of 5 stars
3.6 out of 5 stars
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Most Helpful Customer Reviews
26 of 27 people found the following review helpful
5.0 out of 5 stars Nice, CHEAP book on introductory linear algebra July 26, 2004
This book is a bargain! Do a search on linear algebra and see what comes up; then look at the prices!

This book is a well written exposition of the usual topics one finds in the typical introduction to linear algebra textbook...except at 10% of the price. That in itself is a serious motivation to consider this book -> saving $90 on a book is not to be sneezed at.

OK the book is a dover...that means it's concise, compact, nothing fancy and not overly modern...but that's ok. When you're dealing with the fundementals you don't have to be at the cutting edge. But what you must have is a strong, confusion free understanding of these fundementals. And this book delivers. The proofs are simple and straighforward for the most part (if not terribly expansive) and you should be able to follow them. There are solutions (not worked) for many of the exerices in the book (calcultions type questions, not proofs however). The content can be seen by using the looking inside the book feature.

I have both elementary alegebra by howard anton and this book, and truth be told, I can't see why the price is so different. Anton doesn't give you that much more. I would suggest however that you purchase this is a supplement to your class text (if your lecturer sets work from it), however if you want to do some self-study or brush-up then this little book is perfect (easy to carry too!)

In fact for this book and the linear algebra problem solver (isbn 0878915184), you're looking at $33.50 and between them they cover a large amount of linear algebra. And you're still $82 dollars ahead of ELementary Linear algebra (isbn 0471170550) by anton!

So, in all, an excellent, well-written little book. Fantastic price.
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19 of 20 people found the following review helpful
5.0 out of 5 stars Supplemental Superiority October 28, 2004
As a physics major, i've been told by my E & M teacher that Linear Algebra is one of the two games to be played in physics. (The other naturally being calculus). So, what happens when it comes time to take Linear Algebra and the teacher only serves to confuse the material, and the college textbook is a normal college math book? (a.k.a. not well written or useful). Get Dover books. And this book delivers for me. Everything i'm supposed to learn in Shifrin's text is presented here with much clearer writing. (Especially in drawing your eye to the thereoms, any one who wants to Linear Algebra without knowing the thereoms or applying them to the homework should probably stop now and go back to Trig.) It seems this book would make a good stand alone text, provided you are willing to not expect calculus cookbookness, because it's my side text that trumps my main textbook for 1/10th the price. And in closing, thank God for Dover for making life as a physics major that much cheaper.
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30 of 34 people found the following review helpful
2.0 out of 5 stars You can do much, much better October 12, 2004
First, the text of this book is extremely well-written, the theorems are clearly stated and the proofs are well-presented. Unfortunately, there are LOADS of typos in this book, but that doesn't bother me.

What bothers me are the exercises at the end of each section - the difficulty level of several (not all) of them is far beyond the depth of the text. The text is supposed to be for "undergraduates with little mathematical experience". Don't you believe it. There are problems early in the book that ask you to write proofs that require a depth of understanding that the text does not come close to providing. Many times I was absolutely convinced that the text and the exercises were from completely different textbooks! If the author is going to include difficult or "let's see how well you got this" problems I'm all for it, but at least include some hints in the back to help students get started. Otherwise you're just stranded on your lonely little mathematical island....hungry and cold and completely screwed.

If you just want a book for reference, then this is a very good choice. However, if you are attempting to learn the material and are interested in trying your hand at more than a few problems then I strongly suggest you look elsewhere.
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14 of 14 people found the following review helpful
4.0 out of 5 stars Cheap, formal, well written November 10, 2005
On my desk right now, books by: David C. Lay, Terry Lawson, Sheldon Axler, Klaus Jänich, Robert Valenza, and this one by Schneider and Barker. I tend to go back again and again here.

I'm using this book as a supplement for the textbook in my class. Some of the books cited above don't quite fit the bill because they're so different from the linear algebra for engineering you so often see in classes. But this one is excellent for a matrix-heavy approach.

This book is "bare bones", indeed, but it is very well written. Some might not be used to definitions, propositions, theorems and lemmas but in this case this makes it a whole lot easier for finding (and referencing) the important results. The notation is careful and formal, but the explanations are crystal clear. On the back cover it says it's geared towards students "outside the field of mathematics" but I think they say that because it avoids a purely algebraic approach (like in Valenza where e.g. Ker is defined in the context of group homomorphism). The approach is the one of matrixes, matrixes everywhere (row echelon algorithm, etc.) There are, however, no "modern" applications (such as networks, or ecology) as examples.

Another reviewer complained about the difficulty in exercises. While you have "drill" ones, you do have more conceptual ones, but I think they're on par with the text. There are no pretty illustrations here, and you will see that you don't need them.

In some other books, material might be presented in a wordy manner, but in this book, you just say "ah, so what so-and-so is saying is just Theorem number X.X.X in S&B."

On the whole, this is an excellent acquisition for your undergraduate library. It is cheap and good. What more do you want?
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Most Recent Customer Reviews
5.0 out of 5 stars One of the best math books I've used
In past semesters, the course required text had always been a ridiculously expensive book with many pictures and long, tedious explanations. Read more
Published 17 months ago by Avery
4.0 out of 5 stars Best Math book I ever bought.
Not a bad Math book. It sure doesn't weigh alot. Not taking this math before, it doesn't seem to hard to follow. Read more
Published on May 30, 2012 by troy
3.0 out of 5 stars Somewhat Old
This isn't a bad book. The treatment isn't very rigorous, so it's definitely a book for engineers. The text is a bit small.
Published on April 6, 2012 by Snowball
5.0 out of 5 stars good
very good i like it. it is really good. I would like to recommend it to other people who like it
Published on January 11, 2012 by hx
5.0 out of 5 stars You have to learn to calculate somewhere.
This is not a flashy book. You will not see a lot of fancy symbols, pictures or equations. What you will get is pages upon pages upon pages of matrices. Read more
Published on July 16, 2011 by Odysseus
3.0 out of 5 stars Excessively Formal
Schneider and Barker's book is a very nice reference for those who are already familiar with matrix manipulations and linear algebra. Read more
Published on April 9, 2011 by LostSheep
2.0 out of 5 stars Terrible
this book is terrible, it's confusing and lack of explaination, i recommand u to get the Linear Algebra and it's application by Davie C. Lay
Published on September 2, 2010 by Nat
1.0 out of 5 stars Worst Math book ever run away!
This is the text book for a linear Algebra class and I really wish I dropped the class because of the book. Read more
Published on October 8, 2008 by Kurtis A. Sleeter
2.0 out of 5 stars Surf the web instead.
For about three years, I haven't thought about linear algebra at all. But recently, I've been interested in it again, and went to this book for reference. Read more
Published on June 23, 2005 by theboombody
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