- Hardcover: 584 pages
- Publisher: Wellesley-Cambridge Press; Fifth Edition edition (June 10, 2016)
- Language: English
- ISBN-10: 9780980232776
- ISBN-13: 978-0980232776
- ASIN: 0980232775
- Product Dimensions: 7.7 x 1.3 x 9.2 inches
- Shipping Weight: 3.1 pounds (View shipping rates and policies)
- Average Customer Review: 151 customer reviews
- Amazon Best Sellers Rank: #31,847 in Books (See Top 100 in Books)
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Introduction to Linear Algebra, Fifth Edition Fifth Edition Edition
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Introduction to Linear Algebra, 5th Edition
by Gilbert Strang
Wellesley - Cambridge Press, 2016, ISBN 978-0-9802327-7-6, x+574 pages.
Reviewed by Douglas Farenick, University of Regina
Undergraduate mathematics textbooks are not what they used to be, and Gilbert Strang's superb new edition of Introduction to Linear Algebra is an example of everything that a modern textbook could possibly be, and more.
First, let us consider the book itself. As with his classic Linear Algebra and its Applications (Academic Press) from forty years ago, Strang's new edition of Introduction to Linear Algebra keeps one eye on the theory, the other on applications, and has thestated goal of "opening linear algebra to the world" (Preface, page x).Aimed at the serious undergraduate student - though not just thoseundergraduates who fill the lecture halls of MIT, Strang's homeinstitution - the writing is engaging and personal, and the presentation is exceptionally clear and informative (even seasoned instructors maybenefit from Strang's insights). The first six chapters offer atraditional first course that covers vector algebra and geometry,systems of linear equations, vector spaces and subspaces, orthogonality, determinants, and eigenvalues and eigenvectors. The next three chapters are devoted to the singular value decomposition, lineartransformations, and complex numbers and complex matrices, followed bychapters that address a wide range of contemporary applications andcomputational issues. The book concludes with a brief but cogenttreatment of linear statistical analysis.
I would like to stress that there is arichness to the material that goes beyond most texts at this level.Included are guides to websites and to OpenCourseWare, which I shallcomment upon later in this review. The final page lists "Six GreatTheorems of Linear Algebra." Chapter 7 begins with an informativeaccount of image compression, and would be wonderful material for an undergraduate student to present in a seminar to other students.
Strang's experience at writing and teachinglinear algebra is apparent in the layout of the typeset. Offset in bluetype are topic-specific headings that indicate what is contained in thecontent of the text to follow. For example, on page 5, after developingmaterial on linear combinations of vectors, we find the heading "TheImportant Questions." On page 149, after studying the null space, thereis a subsection with the heading "Elimination: The Big Picture." Eachsection contains the headings "Review of the Key Ideas," "WorkedExamples," "Problems," and "Challenge Problems." These sections areessential reading for the instructor, not just the student. The WorkedExamples include material such as the Gershgorin Circle Theorem, whilethe Problems and Challenge Problems offer the student a chance to master basic ideas and to think much more mathematically about the conceptsunder study. For example, Problem 29 of Chapter 6 asks for thecomputation of the eigenvalues of three matrices (not just genericmatrices, but matrices with structure and, thus, a chance to learnsomething about how the features of the matrix influence theeigenvalues), while Problem 39 of the same chapter asks for the possible values of the determinants, traces, and eigenvalues of the six 3 X 3permutation matrices. There is nothing here that can be said to be dry,uninteresting, or irrelevant; rarely does an undergraduate mathematicstext feel so alive as this one.
This review appeared in the Bulletin of the International Linear Algebra Society, IMAGE Vol.58 (2017) 18-19
Linear algebra is something all mathematics undergraduates and many other students, in subjects ranging from engineering to economics, have to learn. The fifth edition of this hugely successful textbook retains all the qualities of earlier editions while at the same time seeing numerous minor improvements and major additions.
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This book is clearly closed bound to the online course (which I watched briefly). It is not a stand alone book on linear algebra by itself. The book constantly jumps into new concepts without explaining the ideas and bases behind them. If I didn't know that it is the text book for the online course, this book feels more like a note taken by a student during a linear algebra course. I found myself constantly guessing what the the texts in the book are referring to.
I don't want to spend time watching the online videos, that's too time consuming due to the limited time I have. Although I'm able to make progress on this book ( still reading it), the process has been boring. The aspect of finishing this book is not promising. I'm considering finding another linear algebra book.
I think the proper title for this book probably should be something like "Linear Algebra for MIT online course", or "Notes and exercises for Linear Algebra".
The masterful thing about this book is that by adding just a little bit each chapter and connecting it back to the Four Fundamental Subspaces, orthogonality, basis, and linear independence, every new idea is very easy to grasp. The problems range from easy to medium difficulty (though these usually depend on tricks which you may/may not easily get) and help in building your abstraction muscle and thankfully shy away from the tedious computational realm most of the time. I find the way I look at matrices and systems of equations have been forever molded by this book. Perhaps most importantly, and the reason I believe this book is stellar, is that I believe this book is ideal for self-study. I did not even use his online video lectures, I simply did the examples along with him in the book and did all of the problems with solutions in the back. I say this not as a math genius, but as someone with an interest in learning some math a couple of hours per week. This book has given me the confidence to pursue a more abstract treatment of the subject, as well as a numerical linear algebra text which fleshes out the complexity of matrix decompositions and such.