Linear Algebra

by Stephen H. Friedberg, Lawrence E. Spence, Arnold J. Insel

Book Overview

For courses in Advanced Linear Algebra. Illustrates the power of linear algebra through practical applications This acclaimed theorem-proof text presents a careful treatment of the principal topics of... This description may be from another edition of this product.

• Format: Hardcover
• Language: English
• ISBN: 0135371023
• ISBN13: 9780135371022
• Release Date: January 1989
• Publisher: Prentice Hall
• Length: 530 Pages
• Weight: 2.00 lbs.

Customer Reviews

blows you away

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.

Excellent!

I am an undergraduate taking a linear algebra course. The course does not use this book, but my friends introduced this book to me and I simply love it. This book has a very careful treatment of the materials and the order of the materials. It is simply fascinating and this introduces me to the beautiful world of linear algebra. Currently I have nearly finished 4 chapters. The authors explain every concepts very clearly, with some nice inclusions like the maximal principle or similar stuff which broadened my view. The exercises are very nice, while some of them are quite challenging. If there is no challenge at all in the exercise, why should you study that book? The only drawback I can think of is that, it puts some important concepts amid the exercises without careful treatment, e.g. the quotient space. Anyway this is not really a problem if you are willing to learn, because there are many other books which cover those things. For example I use Curtis' linear algebra book to learn quotient space. All in all, this book is simply terrific and fascinating and I recommend all linear algebra novice should start reading this book.

A terrific book on linear algebra

LINEAR ALGEBRA, Third Edition, is one of the better books on linear algebra. The material is presented in an abstract and mathematically rigorous fashion. The focus of the book is on the ideas and proofs behind the linear algebra -- its treatment of applications to physics and computer science is almost nonexistent. Topics covered include vector spaces, linear transformations, systems of linear equations, determinants, inner product spaces, eigenvalues and eigenvectors, and canonical forms.For the aspiring engineering or computer science student, this book is not for you. Basic matrix theory is enough for those fields, and this book is littered with rigorous proofs. There are many other textbooks that present linear algebra from more of an engineering or computer science perspective. As an alternative I recommend that you take a look at "Matrix Analysis and Applied Linear Algebra" by C.D. Meyer. The style of this book is written in the traditional theorem-proof-example style and is thus geared more towards aspiring mathematicians, especially those who enjoy theory and pure mathematics. Many of the examples demonstrate less than obvious inferences and can be very useful, but of course the meat of the book lies in the comprehensive build-up of linear algebra theory from a mathematically sophisticated point of view. In summary, a highly recommended purchase for mathematicians. Computer scientists and engineers should look elsewhere though.

The Best I've Seen

In my experience thus far, I have not come read another introductory algebra that is as comprehensive and thorough as this one. It does not sacrific clarity for the mathematics and similarly it does not sacrifice mathematics for clarity. From the beginning it builds and expects you to keep up as it introduces new topics. There is a definate succession and continuity in this volume which does not exists in many other introductory algebra texts. Furthermore, it presents good proofs and asks for the reader's help where appropriate. The only aspect of the book that I would critique is its problems. Even though they have somewhat challenging ones, there are none which truly test the depths of ones thinking on the material presented. For example, Spivak does this well in his "Calculus". Nonetheless, this is a great book. It covers standard topics with a few applications thrown in for good measure. Even so, it is unmistakebly a math book, not a science/engineering text on mathematics. I would recommend this to anyone who want a solid start in linear algebra.

awesome...i'd give 10 stars

This book combines a very rigorous treatment (with a flavoring of abstract algebra) and interesting applications. The presentation is very clear and straightforward. You get theorems, a proof of each one, and curious exercises. Some exercises also challenge you to develop and prove results about some side topics. As you go through the chapters and learn more, you prove further results. Also, this book is the first which presented Jordan forms lucidly and thoroughly. Other texts shove it into the appendix, which is a mistake, since this topic is important.Finally, the applications are plenty. Standard ones like Markov chains, plus a few fascinating applications, like an entire section devoted to the development of the basics of Special Relativity.This should be the standard text on linear algebra, instead of that drivel by Strang.