Customer Reviews

Linear Algebra Problem Book (Dolciani Mathematical Expositions)

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Halmos is one of the great mathematical expositors of the 20th Century, and his book "Finite Dimensional Vector Spaces" stands as the definitive introduction to the subject for budding mathematicians. This book, "Linear Algebra Problem Book", is perhaps best described as an engaging and semi-informal invitation and complement to that original work, which grew out of lectures given by the legendary John von Neumann. In contrast to typical treatments of linear algebra, "Finite Dimensional Vector Spaces" is abstract (introduces determinants through alternating forms), rigorous, concise, and demands a certain level of mathematical maturity. This book, "Linear Algebra" is exactly the opposite. Starting from very little assumed background, it all but gives away the store, written in plain language, anticipating students' questions and misconceptions, and leading them to a deeper understanding of mathematics through the Socratic method. This is not a problem book in the Schaum's outline sense; there is no drill or rote calculations. Every question is carefully chosen to illustrate a point or expose a potential misunderstanding in the student's knowledge or to exercise the student's intuition and ability to make connections. The answers are given as detailed explanations, integral to the exposition, which go far beyond merely answering the questions posed, raising deeper implications and questions. This is an excellent book for beginning students of higher mathematics, and a very user friendly guide to Halmos' classic text.

I agree with the following reviewer in that Halmos' books are always entertaining and inviting! Fun to read, concise yet clear! The book contains most of the elementary yet important problems in an undergrad course with solutions in the back. It's very helpful working through all these problem because it will tremendous enhance your understanding of the subject. Also, if you want a hardcore problem oriented approach to linear algebra, check out Proskuryakov's Problems in Linear Algebra. Some of the problems in the book are Putnam like. Virtually any type of Putnam taste problems in Linear Algebra can be found in Proskuryakov. But this one, contrast to Halmos', is the least entertaining--that's why it is called HARDCORE PROBLEM APPROACH! You would be a great linear algebra problem solving machine working through both books!

I'm no mathematician but, I own a number of linear algebra and abstract algebra books and this book makes them all pale in comparison. I really enjoyed working through it. Maybe a bit pedantic for more advanced types but, if you want to get a handle on the concepts this is the book.

This is an absolutely excellent book. I came at it before I had ever taken a linear class. The book develops the subject in a way that it seems a natural progression. I was never faced with a proof that seemed to be just number crunching; they all get at the very heart of what is at stake. I recently read back through it after taking a linear class, and I still come to a better understanding of the subject by looking through this. It is well worth your time. The only complaint I have with the book is that there are a lot of typos. It frequently refers back to the wrong problem number, and there are typos in the mathematics that could cause problems if you aren't keeping track of what is happening. (Ex: in the solution to 135, they forget to specify orthogonal projections, or in 145 they say that if y=Px then what is wanted is Uy=Px when it should actually read Uy=Ax) The text is written clearly enough you should be able to figure out what is happening, but if another edition comes out it would be worth upgrading

I'm no mathematician but, I own a number of linear algebra and abstract algebra books and this book makes them all pale in comparison. I really enjoyed working through it. Maybe a bit pedantic for more advanced types but, if you want to get a handle on the concepts this is the book.

This book might just be the best book for self study ever written. The exposition is minimal, covering basic definitions and only a few examples, whenever necessary. The problems are challenging and illuminating. I love the fact that there is a hints section, as well as thorough solutions to each problems. And when I say thorough, I mean REALLY thorough. The first chapter is an excellent introduction to/review of some basic modern algebra (groups, fields) and from there the book dives into linear algebra.

This book is not nearly as thorough as Halmos's Finite-Dimensional Vector Spaces, or even the classic Linear Algebra Done Right, by Sheldon Axler. However, this book might be more instructive than both of them combined.

Highly recommended to anyone interested in linear algebra and who enjoys solving problems.

It is a good book for beginners but not as great for graduate students.