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Introduction to Linear Algebra (Gilbert Strang) 5th Edition
- ISBN-100980232775
- ISBN-13978-0980232776
- Edition5th
- PublisherWellesley-Cambridge Press
- Publication dateAugust 11, 2016
- LanguageEnglish
- Dimensions7.7 x 1.3 x 9.2 inches
- Print length600 pages
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Editorial Reviews
Review
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
Book Description
About the Author
Product details
- Publisher : Wellesley-Cambridge Press; 5th edition (August 11, 2016)
- Language : English
- Hardcover : 600 pages
- ISBN-10 : 0980232775
- ISBN-13 : 978-0980232776
- Reading age : 1 year and up
- Item Weight : 2.58 pounds
- Dimensions : 7.7 x 1.3 x 9.2 inches
- Best Sellers Rank: #479,569 in Books (See Top 100 in Books)
- #102 in Linear Algebra (Books)
- #667 in Probability & Statistics (Books)
- #15,404 in Unknown
- Customer Reviews:
About the author
Gilbert Strang is Professor of Mathematics at the Massachusetts Institute of Technology and an Honorary Fellow of Balliol College. He was an undergraduate at MIT and a Rhodes Scholar at Oxford. His doctorate was from UCLA and since then he has taught at MIT. He has been a Sloan Fellow and a Fairchild Scholar and is a Fellow of the American Academy of Arts and Sciences. Professor Strang has published a monograph with George Fix, "An Analysis of the Finite Element Method", and has authored six widely used textbooks. He served as President of SIAM during 1999 and 2000 and he is Chair of the U.S. National Committee on Mathematics for 2003-2004.
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Top reviews from the United States
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A famous textbook written by Prof. Strang, who teaches linear algebra at MIT for several decades, is recommended by my professor for self-learning linear algebra. This book comes with open-source videos available on the MIT OpenCourseWare.
The replacement arrived and it has the exact same issue. I stop bothering to keep requesting a replacement and accept it as is.
Reviewed in the United States on May 11, 2022
The replacement arrived and it has the exact same issue. I stop bothering to keep requesting a replacement and accept it as is.
The problem with this book is that the author goes too fast. When presenting a concept or an example to a student, one needs to do every step and explain why that step is being taken. Strang omits many intermediate steps, and does not explain how he gets from point A to B. He often does not define terms and the student is left confused as to what he is talking about.
I do not recommend this book unless one is exceptional in math and can make the conceptual jumps the author requires.
I had linear algebra a long time ago and struggled. This book has helped a lot.
Top reviews from other countries
Reviewed in India on February 7, 2024
EDIT: After starting to watch the lectures while reading, I think this is a great resource. Unfortunately I should have been aware of that before writing this review, he's a great professor!