Linear Algebra (4th Edition)

This top-selling, theorem-proof book presents a careful treatment of the principle topics of linear algebra, and illustrates the power of the subject through a variety of applications. It emphasizes the symbiotic relationship between linear transformations and matrices, but states theorems in the more general infinite-dimensional case where appropriate. Chapter topics cover vector spaces, linear transformations and matrices, elementary matrix operations and systems of linear equations, determinants, diagonalization, inner product spaces, and canonical forms. For statisticians and engineers.

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   September 17, 2000
Mohammad (Toronto, Ontario Canada)
8 out of 9 found this review helpful

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.


Good Book for Math and Physics Majors   November 2, 2004
khalee_daal (america)
6 out of 7 found this review helpful

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).


Beautiful presentation !   March 25, 2000
Nishant (Michigan)
13 out of 13 found this review helpful

This book has a lucid treatment of the matrix theory and linear trnasformations of differential equations. although the applications are extended upto Hamiltonians, Markov chains and relativity to name a few. All in all an excellent book which prepares the reader for more specific topics according to reader's taste. Worth reading is the 6th chapter for advanced students intending to major in physics or maths. Definitely worth having one in your shelf. Clear presentation and ample examples will encourage your appetite for matrix theory etc.


awesome...i'd give 10 stars   January 16, 2000
Ted Shane (usa)
20 out of 20 found this review helpful

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.