Customer Reviews

Linear Algebra and Its Applications

5 star:		(35)
4 star:		(11)
3 star:		(6)
2 star:		(8)
1 star:		(21)

 

 

This book was my text for a comprehensive two-semester course in linear algebra I took over ten years ago. To this day, it remains one of my favorites I use as a reference.

The ¡°applications¡± implied by the title has a double meaning. Several simplified yet representative problems taken from engineering and economics are well presented. In addition, another major theme throughout the text is the role of linear algebra applied to other areas of mathematics; notably calculus, differential equations, and optimization. Repeatedly, the author appeals to the reader¡¯s intuition, demonstrating the boundaries between mathematical topics by comparing and contrasting the discrete and continuous case of a problem. For example, the discussion of orthogonal vectors, vector spaces, and projections quickly moves from vectors to functions once we regard functions as infinite dimensional vectors containing infinite components. The discussion eventually leads to a very intuitive take on Fourier series and Legendre polynomials in the context of orthogonal projections. Other examples abound where Strang cohesively ties together various areas of math in a perspective that isn¡¯t emphasized enough in other texts.

Hence, this is not only a book on linear algebra. To get the most out of the text requires familiarity with calculus encompassing multiple variables, vectors and some ordinary differential equations. Readers lacking this background will understand some sections only to be lost in others as coverage moves quickly from elementary concepts to topics where they have no previous exposure.

Chapters 1-5 and half of 6 comprise the core of the book. The remainder provides satisfactory coverage of numerical linear algebra, the finite element method, and linear programming. However, a more thorough treatment of these topics is deferred to Strang¡¯s companion volume, Introduction to Applied Mathematics for which the core chapters provide a good prerequisite.

One more word of caution: The author¡¯s enthusiasm of the subject is both a liability and an asset. Professor Strang sometimes has the annoying habit of summarizing the topic prior to presenting the lesson. Having to weed through his exultation to find where the lesson actually begins makes reading the book challenging at times.

While the rigor in the text may fall short of the needs of pure mathematicians, I see no reason not to recommend this book to anyone seeking a solid foundation for further study in applied mathematics. Getting through the books requires some degree of patience but it¡¯s well worth the effort.

What is it with you people? I see scathing review after scathing review of this book. Do you feel as though it somehow makes you into a real mathematician to belittle the informal tone? Does it make you feel any better about yourself to suggest that the target audience of this text is "kindergarteners?"

Sure, Strang's book may not be an adequate sole text from which to learn linear algebra and matrix theory. But surely serious mathematicians (as opposed to kindergarteners) would never attempt to learn a subject from a single text.

This is where the book shines - as a supplement to a more formal text. (Here, pick your own; I have my own personal favorite, but it has been out of press for years). And then read the two side by side. One provides rigor, the other, INTUITIVE UNDERSTANDING. This, after all, is where Strang's book shines - rather than providing only a formal understanding of the mathematics in question, he manages to convey an intuitive understanding of the objects represented by linear algebra methods in many common applications.

Firstly, this book is true to its title...

It motivates the subject matter clearly and presents instances of why a certain type of problem is important (Why do we care about Ax=b, Ax=[lambda]x, ...)
It motivates the use of certain algorithms (Why do we use Gaussian Elimination, why pivot, why do the SVD, ...)

Also, as a basic text in Linear Algebra, which is THE introductory subject to applied mathematics, it serves a a primer for various areas in applied math: optimization, numerical solution of PDEs, "curve fitting" =), etc.....

I'm shocked at the number of negative reviews of this book. I think it's a great book. Linear algebra is an incredibly important subject, for example in my field of electrical engineering. Every time I need to refresh my understanding of a concept, I turn back to this book (I have the edition from 1976). I had Strang as a lecturer at MIT in the late 1990s, and he is a great teacher, which I think is reflected in his book. I truly enjoy reading this book -- practical, conversational and enjoyable to read, helpful insights, as well as Strang's opinions on the usefulness and practicality of various results. I would describe the book as an advanced introductory linear algebra book, if that makes sense. It's definitely not graduate level, but unless you're pretty sharp, it might be a tough first book from which to learn linear algebra. Maybe that's why there are some negative reviews of this book here. I recommend it very highly, especially for those who already have some knowledge of linear algebra. In fact, the reason I came to this page in the first place is to buy a second copy of the book, so I can have one in my office and one at home... there aren't very many books I would say that about...

I wondered how this book could elicit such mixed opinions, so I took a quick look by reading the first few pages, and scanning the first couple chapters. One can already see the writing style resonsible for this.

Strang is trying to clearly explain the ideas behind the various mechanical constructions, such as Gaussian elmination, in terms of their interpretation via matrices, and also explain practical aspects of the constructions such as cost of implementation, efficiency, and tendency to go "wrong" under roundoff.

This is a lot of ideas to put in a few pages, and students used to books which merely display a mechanical operation, then drill it over and over, are likely stunned by the compactness of the presentation. They are not used to mulling a few succint phrases for meaning, and taking their time. One student reviewer even complained that he had to reread after a few paragraphs, as if that were a bad thing.

He does give very clear and simple examples, he just doesn't give a lot of them. When he has made his point, he does not dwell on it, he moves on to enhance and deepen it. Probably you should work every single exercise in this book.

This is obviously an excellent book from which to learn a lot of deep useful insights into linear algebra and its uses. For those who want more drill on the arithmetic involved, any other book will have a lot of that. But those books will not have the clarity and focus of this book, in most cases. I recommend it highly.

As someone who works in an engineering R&D environment (and is called upon to use linear algebra to solve "real world"
problems), I wanted to put this book in perspective for those who may be unsure of the true value of this book given the variance in the reviews.

1. This book presents an applied treatment of the subject appropriate for a first course. The goal of the
book is to provide the reader with an intuitive understanding of the material. Geometrical arguments and diagrams
are used throughout without apology. Coordinates and matrices are emphasized. Formal proofs are not provided for most results.

2. This book is geared toward those doing computations in the real world. Linear algebra
is the workhorse of modern applied mathematics. Any modern course on linear algebra that does not cover LU, QR, SVD, 4 Fundamental Subspaces,
and least squares is out of touch with reality and in my opinion doing a disservice to those who are paying $$$
for an education. Specifically, those who are ever planning
to get a job in engineering or the mathematical sciences will at some time be expected to solve (or understand how
software like MATLAB solves) least squares problems, systems
of linear equations, eigenvalue problems, linear ODE's, optimization problems, etc... As a result, this book
is focused on matrices and computations. This book is practical in the sense that in the real world - where
numerical solutions are usually required - we are
forced to deal with a basis-dependent
finite-dimensional representation of our problem.

3. Those who require a second course in Linear Algebra covering Jordan Forms, the theory of linear operators, and more advanced material
will not have to unlearn anything from this book. In fact this book is a good stepping stone to further study.
For example, someone who comes to Hoffman/Kunze or Halmos after this book will better appreciate the more
abstract approach based on linear transformations. After all, how can anyone understand or appreciate
a formal abstract treatment of this material before one has a firm grasp of what is being abstracted?

4. Strang, who is a professor of mathematics at MIT, has a Linear Algebra course webpage with video lectures that augment the text and shed additional insight on the material. These
lectures are excellent and really demonstrate the love Strang has for teaching this subject to others.
In my opinion he has done the scientific and engineering communities a big service by writing this book and posting his
video lectures.

5. Strang has another text on Linear Algebra called Introduction to Linear Algebra. Although that text is geared at slightly
a lower level, I like the present text better as a learning tool.
The Intro text is slightly more disjoint in its presentation
and seems to leave more for the reader to discover rather than just presenting the information.

6. The current 4th edition of this textbook has been updated relative to the 3rd edition. I learned the material from the
3rd edition and I actually feel, on the whole, the 3rd edition is a better learning tool as it is geared at a slightly more
rigorous level than the 4th edition.

7. If you really do not like Strang's writing style (which is very conversational and loose, and in my opinion, better
than the dry style of other texts), try Meyer's treatment ("Matrix Analysis and Applied Linear Algebra"). Meyer is more of a traditional text and provides
material for both a first and second course on applied linear algebra (with more emphasis on a second course).

Good luck.

Professor Strang has taught Linear Algebra for many years to legions of one of the United States' top institution. So give him some credit, for starters...
This book is inimitable in its clarity and in how it yields so much insight. I have many books on Linear Algebra and I think this book is worth its weight in gold. I know of no other book that teaches the fundamental subspaces so well.
The book covers standard material in Linear Algebra (and then some) and has a strong matrix-oriented flavor (as opposed to a book giving an algebraic treatment - look for Valenza if you want that).
I don't understand what some of the complaining is about by some reviewers. The book is not abstract enough, not formal enough? No first treatment in Linear Algebra is or should be - that is Linear Algebra 2. Besides, matrices are pervasive in all fields of engineering, physics, applied math and other disciplines and later on the student will advance to even more complex issues (such as numerical linear algebra) and they simply cannot afford not to have seen the standard matrix treatment. In fact, that would be the reason it's so widely taught - because it's so useful. It's no use delving into abstract treatment if one doesn't understand the most basic facts about why it is that you can solve a system of linear equations.
Best of all, his lectures now can be seen on MIT's Open Courseware site.
I have used this book since the second edition. I believe this 4th edition is the best edition yet. Unlike some other books on the market, this new edition is a fully thought-through new edition (Strang has been restructuring his book throughout all editions, ever making this more clear and insightful). Not bloat at all. I wholeheartedly recommend it. In fact, I believe you might get hurt using some other books that are on the market that do a very lousy job on teaching this subject (such as Lay). This book is the gold standard.

It was some years ago when I first took a Linear Algebra course and fortunately the instructor choose this as the text book. I thought that Strang's explanations were superior to the lectures given in class and I could have easily gotten through the course by reading this book and taking the tests ! Just recently I have had to go back and relearn this subject and this book was almost joy to read (well O.K. it is a math book). Mr Strang has the rare ability of making this subject intuitively obvious and convincing. He starts from very a modest beginning of solving systems of linear equations and then makes the almost seamless transition to matrices and vectors by a change of perspective. As the subject is developed, Mr Strang makes every effort he can to clearly present the material as does not defer to the usual "left as a an excercise for the reader" device to evade explaining the subject. The narrative is lively and enthusiatic and sometimes even humorous and has lots of reminders of previously mentioned ideas to keep the text flowing. If more math books were written like this, then fewer people would complain about obscurity of this subject.

First off, this book is not well-suited for students who have never seen a matrix and have not yet mastered the basic calculations of how to multiply and add matrices, or for those who have never seen Gaussian elimination. There are many other textbooks that do nothing but provide you with exercise after exercise of manual computations of inverses and determinants that are better suited to that purpose.

That said, for anyone taking a course in linear algebra who actually wants to know more than the rote mechanics of matrix multiplication and Gaussian elimination, this book provides a succint explanation of what matrices actually represent. And I've held onto the book as a reference now for many years (referring to the 3rd edition).

I came across it as a graduate student studying for doctoral qualifying examinations. Someone suggested that I check out Strang's book from the library as a supplement to my utterly confounding graduate school text. It was a godsend! I pored over Strang's book, doing computations on occasion, and taking copious notes of his thorough explanations of concepts like null space, row space, column space, and eigenvalues. After that, I had no problem passing my qualifying exam in linear algebra!

I am pained at the disappointing reviews submitted. Prof. Strang's work deserves better respect!

I have used this book from 2nd edition onwards for students' perusing a course in Power System Analysis and Digital Protection. I recommend Matlab be used along with the course to understand the different processes in linear algebra, its relation with algorithm development in analysing various stability issues and methods that can provide dimensional reduction of the original problem. It takes time to absorb the work. But once completed, it is a poetry that one can never forget!