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| Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition consists of challenge problems to complement the review problems this have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are utilizing this book, which truly explains this crucial subject. Chapter 1: Introduction to Vectors; Chapter 2: Solving Linear Equations; Chapter 3: Vector Spaces and Subspaces; Chapter 4: Orthogonality; Chapter 5: Determinants; Chapter 6: Eigenvalues and Eigenvectors; Chapter 7: Linear Transformations; Chapter 8: Applications; Chapter 9: Numerical Linear Algebra; Chapter 10: Advanced Vectors and Matrices; Answers to Selected Exercises; Final Exam. Matrix Factorizations. Conceptual Questions for Review. Glossary: A Dictionary for Linear Algebra Index Teaching Codes Linear Algebra in a Nutshell. |
Customer Reviews |
 Gold Standard 2010-07-23 |
| By Mariano Apuya Jr (Kapolei, HI United States) |
I used this book as self study. I was drawn to Gilbert Strang because it seemed to be the gold standard for linear algebra and the popularity is deserved. The one thing I would like to add is the effect of the use of symbolic math software. I used Mathematica but Strang has some code for Mathlab in the book. People have views on this subject but I find that Mathematica does the job well enough. The effect on me is that it made me feel a little insecure by not doing it by hand. Because finding eigenvalues, eigenvectors and row reduction is tedious, I gave in to the temptation of just writing the code which any highschool student can do. While the working Mathematica gave me a good coding skills, I can't help but feel I have some loose ends by relying on the computer too much.
At times I think that doing the problems was mental hazing. I wasn't able to do all of them particularly the more difficult ones. The problems are divided into two parts: the first is the regular problems and the few hard ones. I didn't even touch the hard ones. I good feature of the chapters is at the end there are worked examples where you are given a problem and solve it before you look at the solution.
Finally, Strang's lectures are available at opencourseware at MIT. I think they are also at Youtube. I look back at my self study now and regret not taking advantage of it
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| Decent but not fantastic 2010-07-02 |
| By Xiao Hu |
Pros:
1.The coverage of the four fundamental spaces is fantastic. The pictures showing their dimension, orthogonality etc is very very good and easy to remember. And the importance of the understanding of this topic can not be over emphasized. Prof Strang did an excellent job here.
2.The on-line lectures are excellent. Well at least for most of them.
Cons:
The SVD part is not excellent. Prof. Strang agrees that this is the climax of linear algebra. But the presentation of this critical topic is not excellent. The link between the four fundamental spaces and SVD is not so clear. And the related pseudo-inverse is also not so excellent. Unfortunately, the video on SVD also suffers from the same problem. But I would not blame too much on the video. After all, I am not sure if an excellent coverage of SVD can be given within one lecture. But the book should have plenty of space for a good coverage.
For a good SVD coverage, I found the following is good.
1) A good understanding of the four fundamental spaces is very important. Prof. Strang does an excellent job in his book.
2) Some internet articles actually provide good introduction, better than those provided in books
3) An article on-line by Dan Kalman is very comprehensive but not the first thing you should read.
4) Trefethen in his Numerical Linear Algebra has some good (but not complete) description. |
| School Book 2010-03-25 |
| By Crystal Pepper |
Easy to read.
Very informative.
Sometimes would leave you guessing though. Not enough examples. |
| Good Book but with unclear parts (then watch the lectures) 2010-03-03 |
| By Eduardo (Brazil) |
| The book is half very good and half with unclear parts. Some topics are explained in a very clear and nice way. Other topics are unclear. One example is in page 334 where the author tries to prove that a symmetric matrix always have eigenvalues signs that match the pivot signs. The authors asks the reader to look at the changing of values while they "moves to zero". I still can't see this "move to zero" in the matrix multiplication. In other sections he talks about a topic that is only explained further in the book. One example is in page 310 exercise 31 when the author tasks you to work with the Cayley-Hamilton Theorem, but the theorem is only stated clearly in a following exercise. But I would like to note that things that are not well explained in the book are better explained in his lectures. So if you choose to buy the book I would recommend you to watch the video lectures, which are nice. |
| Fantastic! 2010-02-19 |
| By Adson F. Da Rocha (Brasilia, Brazil) |
I used this book in my Linear Algebra class, and my students, even some that failed the course before, told me they finaly understood Linear Algebra.
With all due respect, I don't know how someone can give it less than five stars. Since the beginning, the book develops, in the student, a strong intuition, which allows him/her to develop slowly and steady. Each topic advances the knowledge just the right amount.
Also, the book has a set of companion youtube lessons that are among the best lessons I have ever seen - it is good not only for students but also for professors who want to learn how to became better teachers.
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