Product Description

Linear algebra is a living, active branch of mathematics which is central to almost all other areas of mathematics, both pure and applied, as well as computer science, the physical and social sciences, and engineering. It entails an extensive corpus of theoretical results as well as a large body of computational techniques. Unfortunately, in recent years the content of the linear algebra courses required to complete an undergraduate degree in mathematics has been depleted to the extent that they fail to provide a sufficient theoretical or computational background. Students are not only less able to formulate or even follow mathematical proofs, they are also less able to understand the mathematics of the numerical algorithms they need for applications. Certainly, the material presented in the average undergraduate linear algebra course is insufficient for graduate study. This book is intended to fill this gap by providing enough material "theoretical and computational" to allow the student to work independently or in advanced courses.

The book is intended to be used in one of several possible ways:

(1) as a self-study guide ;

(2) as a textbook for a course in advanced linear algebra, either at the upper-class undergraduate level or at the first-year graduate level ; or

(3) as a reference book.

It is also designed to prepare a student for the linear algebra portion of prelim exams or PhD qualifying exams.

The volume is self-contained to the extent that it does not assume any previous formal knowledge of linear algebra, though the reader is assumed to have been exposed, at least informally, to some basic ideas and techniques, such as the solution of a small system of linear equations over the real numbers. More importantly, it does assume a seriousness of purpose and a modicum of mathematical sophistication on the part of the reader. The book also contains over 1000 exercises, many of which are very challenging.

Customer Reviews (2)

Outstanding

This is an excellent introduction to graduate-level linear algebra, touching on theory, applications, and algorithms. It's one of those books I wish had been available when I was in grad school.

wonderful for prelims
This book is absolutely terrific for preparing for prelims.The best of its kind available. ... Read more

Product Description
There are a number of very good books available on linear algebra. From this one might deduce that the existing books contain all that one needs to know in the best possible form and that any new book would just repeat material in the old ones. However, new results in linear algebra appear constantly, as do new, simpler, and better proofs of old results. Many linear algebra results obtained in the past thirty years are accessible to undergraduate mathematics majors, but are usually ignored by textbooks. In addition, more than a few interesting old results are not covered in many books. In this book, Prasolov provides the basics of linear algebra, with an emphasis on new results and on nonstandard and interesting proofs. The book features about 230 problems with complete solutions. It would be a fine supplementary text for an undergraduate or graduate algebra course. ... Read more

Customer Reviews (1)

A good book on finite dimentional linear algebra
The book opens with determinants ... excepted for this point, I think this book is worth the money it costs.

All you need to know in linear algebra at undergraduate level is here. ... Read more

Product Description
This is a highly readable self-contained textbook intended for upper level courses in linear algebra. The notations and terminologies are very clear and concise. The examples and exercises of different levels are well designed and will help the reader to grasp and understand the subject theoretically and computationally. An earlier introduction to linear algebra is not necessary to appreciate the book.

All the concepts and topics of matrices, sets and elementary abstract algebra needed for subsequent use are included. The book also contains examples and counter-examples of the concepts used in the text. The emphasis throughout is on a holistic understanding of linear algebra and therefore the overall tone of the book is rigorous and advanced but also clearly defined and highly approachable.

The author has drawn upon his many years experience of teaching the subject to write a book that will be valued by all keen mathematicians.

Contents

1. Matrices and Linear Equations 2. Sets and Algebraic Structures 3. Vector Spaces, 4. Linear Transformations 5. Algebra of Linear Transformations 6. Dual Spaces 7. Diagonalization 8. Inner Product Spaces 9. Bilinear and Quadratic Forms

Also available:

Bayesian Statistics And Its Applications - ISBN 190574000X
Differential Geometry of Curves and Surfaces in E3 - ISBN 1905740549

Anshan Publishers is a publisher of fine medical, scientific, and technical books. We find the best titles from our worldwide publishing partners and bring them to the global marketplace.

We publish in a wide range of fields, including:-

Biological Sciences
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Product Description
Beginning from scratch and developing the standard topics of Linear Algebra, this book is intended as a text for a first course on the subject. The goal to which this work leads is the Theorem of Hurwitz - that the only normed algebras over the real numbers are the real numbers, the complex numbers, the quaternions, and the octonions. Unique in presenting this material at an elementary level, the book stresses the complete logical development of the subject and will provide a bavuable reference for mathematicians in general. ... Read more

Customer Reviews (1)

An illuminated, highly concentrated review of Linear Algebra
From a physics undergrad: This is one of those wonderful, highly concentrated books that deliver extensive Wisdom in only a few pages of hardcore, to-the-point Theory, without simplifying. If you enjoy being told things in a frank manner and without excessive preambles, even if this means slower reading, this book is for you. The theory is built from scratch, but a lack of general abstract mathematical culture might prove problematic. Not recommended for the unprepared or those greedily seeking immediate applications. ... Read more

Product Description

Elementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study.

The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, exploring a comprehensive range of topics.

Product Description
As the basis of equations (and therefore problem-solving), linear algebra is the most widely taught sub-division of pure mathematics. Dr Allenby has used his experience of teaching linear algebra to write a lively book on the subject that includes historical information about the founders of the subject as well as giving a basic introduction to the mathematics undergraduate. The whole text has been written in a connected way with ideas introduced as they occur naturally. As with the other books in the series, there are many worked examples.

Solutions to the exercises are available online:
* The full set of solutions for lecturers only is available for download on a password protected website at http://textbooks.elsevier.com/
* readers are freely accessible at http://books.elsevier.com/companions/0340610441. ... Read more

Product Description
This book presents a unified treatment of recently developed techniques and current understanding about solving systems of linear equations and large scale eigenvalue problems on high-performance computers. It provides a rapid introduction to the world of vector and parallel processing for these linear algebra applications. Topics include major elements of advanced-architecture computers and their performance, recent algorithmic development, and software for direct solution of dense matrix problems, direct solution of sparse systems of equations, iterative solution of sparse systems of equations, and solution of large sparse eigenvalue problems. This book supercedes the SIAM publication Solving Linear Systems on Vector and Shared Memory Computers, which appeared in 1990. The new book includes a considerable amount of new material in addition to incorporating a substantial revision of existing text. ... Read more

Product Description
Designed for use by sophomore engineering or junior physical science majors, this text is suitable for an introductory course in linear algebra and differential equations or a course in differential equations with a linear algebra prerequisite. This text contains detailed coverage of applied topics and includes theorems specifically applicable to engineering students. There is a new chapter on "Stability and the Phase Plane", approximately 300 new problems added throughout and several BASIC programs on numerical solutions of differential equations are included. ... Read more

Customer Reviews (13)

The ABSOLUTE WORST Math text I've ever come across!!!
As most other reviewers have pointed out, this book is AS BAD AS IT GETS. Most chapters have very simple (or nonexistent) examples, and the explanations, theorems and proofs are presented in an extremely poor and confusing fashion. I'm a "self-study" kind of person, and am very good at Math (got high As in Calc I, II and III - multivariable). So, as some others seem to insinuate on here, I'm not a "disenchanted" student looking for a free ride. I would love to get into the detail of things, but if the book doesn't explain anything properly, how the hell are you supposed to learn the material??? Besides, the more difficult and complicated the material, the more intricately and thoroughly it should be explained. This book simply glosses over things and leaves everything else to your imagination. Like some said earlier, this book should be burned and banned from publication!!!

An Excellent Beginners Book.
This book is excellent.I'm shocked at the low ratings, BUT I think I can explain why.This is one of the best introductory books out there.I used it in my first class as an engineering student before I switched over to a mathematics major.Classes for math majors don't normally use this book because it is too elementary.But for non-math majors (engineering, chemistry, physics, ...) this is the first book of choice.Unfortunately, these majors are also full of people in the early years who won't like differential equations.Therefore, this book gets a lot of negative attention from disenchanted students.I love differential equations, but many people who see themselves as good in math get an unexpected bad grade in this class--they can't accept that and instead fault the book or the teacher.I admit, differential equations seemed to me at first to have too much clever guessing, no single structured methodology with which to apply to every differential equation, and most annoying is that most differential equations can't be solved in closed form anyway.This situation is not the fault of the book.Even today there are folks getting PhD's by working on unsolved differential equations.

For those who want more help, I believe in having lots of practice problems.So, in addition to this book, get the "Schaum's Outline of Differential Equations" by Bronson (ISBN: 0070080194) for slightly more than $10 (cheap).Also, I believe in reading more than one source simultaneously, so get "Ordinary Differential Equations" by Tenenbaum and Pollard (ISBN:0486649407) (Also cheap), and read it along with Rabenstein's book.Tenenbaum's book might be just as good or better as Rabenstein's book, so it might be wise for the instructor to use Tenenbaum's book instead of Rabenstein's book and help the student save some money.But I suspect Rabenstein's book is still more elementary in treatment.

Not worth your money.
This book doesn't explain s***! It's the worse math book out there. To many theorems and not to many problems. Look for another ODE & Linear Algebra book if you can.

I disagree with the other reviewers....
I think the other reviewers all looked at this book from the perspective of an engineering major who wasn't interested in learning the topics but just wanted to get through a required course without having to put in the effort to understand the material. This book does an excellent job of tying together the two topics at hand. Yes, like any good math book, there are lots of proofs. Of course, I'm reading this from the perspective of a graduate student in geochemistry with a bachelors degree in math from several years ago. It's a great reference/review book for me. So, I'd just like to counter the other reviewers by saying if you're looking for a book with a good concise theory based introduction to Differential Equations and Linear Algebra, this is the best one I've seen.
One final note -- I think this web form is screwy, I can't correct the repeated sentence above...

just about worst math book i have used
I used this for a introductory differential equations course. All the reviewers are dead on. This book will make you hate math with a passion such as you have never known. ... Read more

Product Description
This book covers the material of an introductory course in linear algebra: sets and maps, vector spaces, bases, linear maps, matrices, determinants, systems of linear equations, Euclidean spaces, eigenvalues and eigenvectors, diagonalization of self-adjoint operators, and classification of matrices. The book is written for beginners. Its didactic features (the "book within a book" and multiple choice tests with commented answers) make it especially suitable for self-study. ... Read more

Customer Reviews (2)

Concise.
How can you pack an entire introductory course in linear algebra into under 200 pages AND make it enjoyable to read? Janich knows how. There is virtually zero fluff here. This is both good and bad, however. Janich teaches you what you need to know, and doesn't waste time explaining the same thing 10 different ways. The down side is that if you don't get a concept straight away, you'll feel lost.

There is a distinct lack of examples and exercises, and the exercises that are given have no solutions provided. This means that it is very hard to rectify any misunderstandings you may pick up.

This book makes for an excellent companion text, and serves admirably for review purposes. But if you need to learn how to apply the abstract concepts, you will want a second text that contains plenty of examples and exercises. As a lecturer once told me: Mathematics is not a spectator sport. You have to do it, not just read about it.

A must have for any first course in linear algebra
This book presents in a very simple and lucid way the terminology and concepts of linear algebra as they would be used by any mathematician, but presents it in such a way that it is extremely accessable to theundergraduate first course in linear algebra. I used this along with the"required" text for my linear algebra course and found this farsuperior. It doesn't waste any time on useless details i.e. solving systemsof equations, "finding" the inverse, determinant or any form ofrote calculations or the ridiculous identity "proofs"etc... whichabout 50% of every other undergrad linear algebra texts I've seen or useddo (he does touch on GE a little). If you're planning of studying mathseriously, or are interested in math then this book is definitely a keeper.Another thing I liked about this book is that it doesn't act like atextbook, one can easily sit down and just "read" it, owing againto Janich's unique style. ... Read more

Product Description
The unique feature of this compact student's introduction is that it presents concepts in an order that closely follows a standard mathematics curriculum, rather than structure the book along features of the software. As a result, the book provides a brief introduction to those aspects of the Mathematica software program most useful to students. The second edition of this well loved book is completely rewritten for Mathematica 6 including coverage of the new dynamic interface elements, several hundred exercises and a new chapter on programming. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. In addition to its course use, this book will serve as an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time. ... Read more

Customer Reviews (5)

Fast and useful manual...cheap too
Needed this for a math lab course. Not much to say other than it came in really fast and in great condition... though I'm sure I would only be using it for this semester only.

an excellent introduction
I read through this quickly today and found it very informative, if alittle short
on 'wow' factor. Learning Mathmatica depends on gaining a command of its
quirky syntax and i thought the author did a good job of guiding the reader through
an interesting array of examples in precalc, calc and lin alg, nicely driving home
various syntax issues in multiple contexts. Graphing and Manipulate functions get
special attention. The threshold issue on help books is "is this better than the
documentation". The answer is a decided yes. I might have wished for some extended
problem examples--like newton's method, or pendelum problem--that lend themselves
to the mathmatica notebook format. Minus one star for an unsatisfactory introduction
to wolfram programming. Overall--a very readable and likable presentation of an
exciting software. Addendum: added back a star after visiting the website and
downloading the reference notebooks--an awesome collection of syntax.

Wonderful supplement
Being that Dr Bruce Torrence is my academic advisor at Randolph-Macon College, my opinion is obviously biased.However, I do know for a fact that both authors have worked with Mathematica in its many iterations and are very good at what they do; they have watched the software grow and expand and, as such, are very familiar with the program.An excellent supplement for his classroom, this book is a brilliant introduction as well as reference for new and old Mathematica users alike.

Just right!
This is the perfect start for someone who knows a modest amount of this math and nothing about Mathematica. The exercises flow logically and I find them fun to do. I tried a few other guides and zzzz!

A Great First Step
This book is designed to jump start the reader's experience with Mathematica. Since people learn best by example, reviewing "basic" math examples (Algebra, Calculus, and Linear Algebra) provides a "painless" introduction to the new environment. This book is not intended to be complete in any sense. But it WILL make you feel comfortable with the daunting new interface of Mathematica.

This is the only Mathematica book that I have finished. It was a great introduction, and I still use as a reference.

If you are thinking about buying Mathematica--DON'T get it without some introductory book. This one as a good start. ... Read more

Product Description
Linear algebra permeates mathematics, perhaps more so than any other single subject. It plays an essential role in pure and applied mathematics, statistics, computer science, and many aspects of physics and engineering. This book conveys in a user-friendly way the basic and advanced techniques of linear algebra from the point of view of a working analyst. The techniques are illustrated by a wide sample of applications and examples that are chosen to highlight the tools of the trade. In short, this is material that the author wishes he had been taught as a graduate student. Roughly the first third of the book covers the basic material of a first course in linear algebra. The remaining chapters are devoted to applications drawn from vector calculus, numerical analysis, control theory, complex analysis, convexity and functional analysis. In particular, fixed point theorems, extremal problems, matrix equations, zero location and eigenvalue location problems, and matrices with nonnegative entries are discussed. Appendices on useful facts from analysis and supplementary information from complex function theory are also provided for the convenience of the reader. The book is suitable as a text or supplementary reference for a variety of courses on linear algebra and its applications, as well as for self-study. ... Read more

Product Description
This book describes basic methods and algorithms used in modern, real problems likely to be encountered by engineers and scientists - and fosters an understanding of why mathematical techniques work and how they can be derived from first principles. Assumes no previous exposure to linear algebra. Presents applications hand in hand with theory, leading readers through the reasoning that leads to the important results. Provides theorems and proofs where needed. Features abundant exercises after almost every subsection, in a wide range of difficulty. A thorough reference for engineers and scientists. ... Read more

Customer Reviews (6)

Waste of my 36 dollars
Similar to the other student who reviewed this, I am a student at the University of Illinois and was seeking help from this solution manual thinking that it would contain the answer to even problems and maybe even some work. I was utterly disappointed and even angry that this solution manual was such a waste of my money. Chances are that if you plan on buying this solution manual then you already have the book in which it already contains almost ALL of the same things that this solution manual tells you. It writes the exact same thing and is of absolutely no help to me so far. This has been one of the biggest wastes of my money and i hope that the writers of this solution manual can be smarter and actually put something useful that you can't get from the book.

REVIEW OF APPLIED LINEAR ALGEBRA TEXTBOOK
I am using this book for my class at teh University fo Maryland.
It is a very good book for Application of Linear Algebra students.
Easy to read and plenty of meaningful exercises

Applied Linear Algebra
I am very pleased with the product.It is in excellent condition, consistent with the description online.

Poorly Organized and Sorely Lacking Concrete Examples.
I used this book for a course at U. of Illinois, and the book is too conceptual and poorly organized for students with no prior knowledge of Linear Algebra.Far too many of the problems are proofs, which seems more appropriate for very advanced students.Moreover, the book introduces many concepts without providing ANY concrete sample problems.

Olver's true deficiency, however, is the jumbled and inconsistent organization.The book frequently requires students to solve problems with concepts that the book has not yet introduced.For example, the book asks students to find Least Squares solutions on page 184, but does not demonstrate how to find LS solutions until page 195 (2 sections later).

Additionally, most books provide answers to even or odd numbered problems, but the selection of answers in this book's answer key is completely random.It will provide answers to even or odd problems, and sometimes only to parts.

In brief, this book satisfies Mathematicians who enjoy primarily conceptual discussions and proofs, but will frustrate and confuse students with no background in Algebra (even those who have taken Calc 3).I would avoid it, if possible.

making some justice
I used this book as an undergrad and I just LOVED IT. I was able to follow what the author was saying, and after reading each section I was able to complete the excercises. I really find it hard proving theorems and that, and I don't think this book focuses on that. I learned a LOT from this book. It just spoke to me! ... Read more

Product Description
This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and Gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others are conceptual. ... Read more

Customer Reviews (11)

Missing Pages
I started using this book as it was the assigned for a course. However, it's mid-semester, and I realized my book is missing pages! I'm pretty sure it's a binding issue....

I'm very disappointed, and it's a huge annoyance to pay for a textbook that is missing pages. I wanted to study for an upcoming an exam, but will have to borrow a friend's book in the meantime. Do not buy this book, get the hard-copy book if possible.

A good math textbook
This book is easy to understand, and very concise.There are a few printing errors, but I'm pleased with it.The answers are in the back of the book, but sadly no hints or detailed solutions.My professor chose to provide those as additional course materials, which I have found helpful.

Overall, a better than average math text.

A nice introduction for students of pure mathematics.
Serge Lang's Introduction to Linear Algebra provides a nice introduction to the subject.The text, which is designed for a one semester course for students whoare taking or have completed multi-variable calculus, covers the basic theory and computational techniques.Since the emphasis is on proving theorems rather than the applications that are of interest to physical scientists, engineers, and economists, the text is best suited to pure mathematics students.

Topics are motivated, the theory is carefully developed, computational techniques are demonstrated through clearly written examples, and geometric interpretations of the algebra are discussed.The exposition is generally clear, but I occasionally had to turn to Blyth and Robertson's Basic Linear Algebra 2nd Edition or Friedberg, Insel, and Spence's Linear Algebra (4th Edition) for clarification when examples were lacking (notably in the section on eigenvalues and eigenvectors that precedes the introduction of the characteristic polynomial).Another caveat is that there are also numerous errors, including some in the answer key.

The exercises consist of computational problems, which require meticulous attention to detail, and proofs of results that extend the topics developed in the text. The exercises are organized thematically in order to teach concepts not covered in the body of the text. Some problems are reintroduced after additional material has been developed, so that you can solve them in new, more efficient, ways, thereby demonstrating the power of the new techniques that you are learning.Answers to most of the exercises are provided in an appendix, making the text suitable for self-study.

The text begins with a review of vectors.This material is drawn from Lang's Calculus of Several Variables (Undergraduate Texts in Mathematics) and should be familiar to most readers.Next, Lang demonstrates how matrix algebra can be used to solve systems of linear equations.While the reader presumably learned how to solve systems of linear equations in high school (or even earlier), the discussion of homogeneous linear equations, row operations, and linear combinations provides the foundation for subsequent topics in the book.

The remainder of the book is devoted to finite-dimensional vector spaces.Once Lang introduces the basic definitions, he covers linear independence, the basis of a vector space, and dimension.This leads to a discussion of linear mappings, their representation by matrices, and how the kernel and image of these maps are related to the rank of the matrix of linear transformation.Lang discusses composition of mappings and inverse mappings before delving into scalar products, orthogonal bases, and bilinear maps.Lang then develops the theory of determinants and discusses how to apply them to solving systems of linear equations, finding the inverse of a matrix, and calculating areas and volumes.After introducing eigenvectors, eigenvalues, and the characteristic polynomial, Lang concludes the book with a discussion of the eigenvectors and eigenvalues of symmetric matrices that uses the earlier material on scalar products and orthogonality.

Much of this material is drawn from Lang's Linear Algebra (Undergraduate Texts in Mathematics), where it is treated in more depth.However, that text is written for students already familiar with basic matrix manipulations, so it does not discuss elementary matrices or Gaussian elimination.Understanding it also requires greater mathematical sophistication.

This text is limited in scope.If you are preparing to do graduate work in mathematics, you will need to read an additional text such as Lang's Linear Algebra, Friedberg, Insel, and Spence's Linear Algebra, Hoffman and Kunze's Linear Algebra (2nd Edition), Axler's Linear Algebra Done Right, or Blyth and Robertson's Further Linear Algebra.Of these, the one that is most suitable for self-study is Further Linear Algebra.

If you are interested in an introductory text that is suitable for self-study, you may wish to consider Blyth and Robertson's Basic Linear Algebra as an alternative to this one, as it includes abundant examples and answers to almost all the exercises.

Marginal Text
I used this book for a college-level linear algebra course and found it marginal. Although the author is clear, he skips steps and does not provide ANY answers to exercises in the back of the book. Sometimes you can find the answers to exercises in proofs contained in subsequent chapters. You really need a good professor (which I thankfully had) to get the most out of this course and book.

Too Concise (3.5 Stars)
This book was used in our intro to linear algebra for math/physics majors, and it was decent, but not great.The book is very concise, so you can easily read it before your lecture and then again after lecture (most sections are about 5 pages).However, this also leads to some things not being hammered in, or not emphasized as much as they should be.Also, there are very few examples of actual problems, and the reader is often left having to do something concrete from the theory with no examples.This is a tad annoying, but is good in that it makes you think.However,there are a few errors in the answers in the back of the book.So there were a few times I did what I thought was the logical way to do a problem, and my answers were not the same as the books, but mine were correct.These errors in the book were very annoying, but the actual text, for the most part, had few errors.The style of writing is fine, and to the point.

Overall, the book is decent, but I am sure there are better books out there. ... Read more

Product Description

Thanks to the advent of inexpensive computing, it is possible to analyze, compute, and develop results that were unthinkable in the '60s. Control systems, telecommunications, robotics, speech, vision, and digital signal processing are but a few examples of computing applications. While there are many excellent resources available that focus on one or two topics, few books cover most of the mathematical techniques required for a broader range of applications. Fundamentals of Linear Systems for Physical Scientists and Engineers is such a resource.

The book draws from diverse areas of engineering and the physical sciences to cover the fundamentals of linear systems. Assuming no prior knowledge of complex mathematics on the part of the reader, the author uses his nearly 50 years of teaching experience to address all of the necessary mathematical techniques. Original proofs, hundreds of examples, and proven theorems illustrate and clarify the material. An extensive table provides Lyapunov functions for differential equations and conditions of stability for the equilibrium solutions. In an intuitive, step-by-step manner, the book covers a breadth of highly relevant topics in linear systems theory from the introductory level to a more advanced level. The chapter on stochastic processes makes it invaluable for financial engineering applications.

Reflecting the pressures in engineering education to provide compact yet comprehensive courses of instruction, this book presents essential linear system theoretic concepts from first principles to relatively advanced, yet general, topics. The book’s self-contained nature and the coverage of both linear continuous- and discrete-time systems set it apart from other texts.

Product Description
Deals almost exclusively with real finite dimensional vector spaces & in particular with the principal axis theorem which follows a straight path to its solution.DLC: Algebras, Linear. ... Read more

Customer Reviews (3)

Sophomore Level ???
This book is very confusing. The reader is required to make very large leaps to relate example to exercise. Most of these leaps (chap 2-6) involve wading through set theory instead of applying what was covered in a given chapter. It seems as if the questions are designed so the reader must figure out some "trick" in order to solve the problem. This book may be useful if the reader is very familiar with logic notation, set theory, and linear algebra; otherwise, you will probably spend a lot of time learning these things from other sources.

A Terrible Textbook
This book is god-awful.The author will use the same symbol to mean many different things, and won't bother to explain the new terminology if he's used it within the past couple of pages.

It's impossible to open the book and pick the important bits out of each chapter - theorems, proofs, and examples all look the same. If you want to find that theorem you think you saw several pages ago, you have to skim very carefully.

The exercises at the end of each chapter are all complete wastes of time. Invert a 5x5 matrix! You won't learn anything useful in the process, but it'll take you a while to get there!

If you want to learn linear algebra, just read mathworld and wikipedia instead of buying this book.

A very good on linear algebra!
I found the book to be very thorough and well written. It seemed very easyto understand except for thechapter on Jordan Canonical Forms. However, Iwould not recommend this book to someone who is learning it for the firsttime, unless they have a high degree of mathematical maturity. Try thebeginner book by Howard Anton. ... Read more

Product Description

This text is designed to resolve the conflict between the abstractions of linear algebra and the needs and abilities of the students who may have dealt only briefly with the theoretical aspects of previous mathematics courses. The author recognizes that many students will at first feel uncomfortable, or at least unfamiliar, with the theoretical nature inherent in many of the topics in linear algebra. Numerous discussions of the logical structure of proofs, the need to translate terminology into notation, and suggestions about efficient ways to discover a proof are included. This text combines the many simple and elegant results of elementary linear algebra with some powerful computational techniques to demonstrate that theorectical mathematics need not be difficult, mysterious, or useless. This book is written for the second course in linear algebra (or the first course, if the instructor is receptive to this approach).

... Read more

Customer Reviews (3)

Average resource
I used this book in a math class and only purchased it because I am familar with the organization and layout of concepts in the book.The author writes the book that may be confusing to the first time student of linear algebra.If you are to use this book, I suggest to also pick up a copy of another linear algebra book that may concentrate on definitions and simpler proofs in the begining of the book.

Good reference book, poor learning tool.
While Messer shows good logic on how to impliment proofs, he fails to make good definitions of common terms.Most of the in text examples have nothing to do with the chapter they are in andare often so over simplified that it is impossible to extend the idea.The only reason that this book gets 2 stars is because it has a decent answer section.

Wonderful introduction to Linear Algebra and Math Proofs
We've used this book in our freshman course in Mathematics (Linear Algebra) at University of Copenhagen, Denmark. It's very good as a introduction to Mathematical Proofs too. ... Read more

Product Description
A unique, applied approach to problem solving in linear algebra

Departing from the standard methods of analysis, this unique book presents methodologies and algorithms based on the concept of orthogonality and demonstrates their application to both standard and novel problems in linear algebra. Covering basic theory of linear systems, linear inequalities, and linear programming, it focuses on elegant, computationally simple solutions to real-world physical, economic, and engineering problems. The authors clearly explain the reasons behind the analysis of different structures and concepts and use numerous illustrative examples to correlate the mathematical models to the reality they represent. Readers are given precise guidelines for:
* Checking the equivalence of two systems
* Solving a system in certain selected variables
* Modifying systems of equations
* Solving linear systems of inequalities
* Using the new exterior point method
* Modifying a linear programming problem

With few prerequisites, but with plenty of figures and tables, end-of-chapter exercises as well as Java and Mathematica programs available from the authors' Web site, this is an invaluable text/reference for mathematicians, engineers, applied scientists, and graduate students in mathematics. ... Read more

Customer Reviews (1)

Good book!
A linear combination of vectors allows any coefficient - positive or negative. A more powerful concept is the "cone" of a set of vectors which allows only positive combinations (more powerful because a linear space is the union of two cones, but a cone can never be expressed as a linear space). While there are many many good books on the "algebra of linear spaces" (i.e. Linear Algebra) I havent seen any that treat the "algebra of cones" with the thoroughness that this book does. I found this book useful to derive existence proofs in combinatorial optimization although the material is fundamental enough to be applied in many more fields. Best used if you have a reasonably good grasp of linear algebra. ... Read more