Matrices and Linear Algebra

This book provides a solid first course on linear algebra for math majors and theoretically inclined students of physics and engineering. It covers the standard topics - simultaneous linear equations, vector spaces, determinants, linear maps, eigenvalues and eigenvectors, the Cayley-Hamilton theorem, and Jordan form - at a fairly rigorous and abstract level, like most Dover titles. To wit, there is very little hand-waving, there are almost no pictures, and few applications of the material are given. (The final chapter does discuss systems of linear differential equations.) The exercises comprise both drills and proof-type questions. The style and difficulty of problems should be palatable to first year math students, but may intimidate others. For adventurous scholars, the book includes more advanced material on elementary symmetric functions, complex inner product spaces, Moore-Penrose pseudoinverses (called 'natural inverses'), and an enjoyable 'prove-it-yourself' section on normal matrices and polar decomposition. Overall, a very solid textbook at an outstanding price.

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?

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.

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. <br /> <br /> 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. <br /> <br /> 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!) <br /> <br /> 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! <br /> <br /> So, in all, an excellent, well-written little book. Fantastic price. It's easy to follow and learn from and covers most if not all (depending on your lecturer) of a first course in linear algebra (check the table of contents!). Even has end of chapter quizzes, with answers (10 true/false, 5 multiple choice questions) So check it out! What's $12, really? That'll get you 1/10 of the Anton book but all of this!

This book is very useful not only as an introduction to the college math but also as an alternative high school book. One of the best investion I have ever made! Get it - now.