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I need a better Linear Algebra book

  1. Oct 27, 2009 #1
    I am currently using Gilbert Strang's "Linear Algebra and its applications" and am finding the book to be very terrible, there are very few examples in the section introductions and no 2 problems seem to relate, the author loves to hide how to do things all over the book or sometimes in the drawings without even explaining anything. The solutions manual is no help either because sometimes the author just seems to be pulling numbers out of his @$$ or doesn't even do the right problem based on the instructions given.
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  3. Oct 27, 2009 #2


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    I have the third edition of Strang and I do not like it either though it is better by far than Matrix Theory with Applications by Jack L. Goldberg. In fact Stang is the best book of its type at its level that I am aware of. I don't know what you mean by the problems not being related, could you give an example?

    My standard recommendations are

    Finite-Dimensional Vector Spaces by P.R. Halmos
    Linear Algebra Done Right by Sheldon Axler
    Linear Algebra by Georgi E. Shilov
    Linear Algebra (Undergraduate Texts in Mathematics) by Serge Lang

    It depends on your goals though, can you be more specific? Those books are more theoretical than Strang. None of those really replace Strang though as it (in my view pointlessly) stresses routine numerical calculations.
    A good start would be

    Introduction to Linear Algebra (Undergraduate Texts in Mathematics) by Serge Lang

    I have also read through Linear Algebra with Applications by Anton it has all those numerical examples, though it does not really improve on Strang idividual opinions vary. The best thing if you do not know exactly what you are looking for is to flip though 10-12 books at the library to see which one fits your individual style.
  4. Oct 27, 2009 #3
    I also like the books by Lang and Shilov. If cost is not an issue, Linear Algebra by Friedberg, Insel et al. is a good one as well ( at least I think so).
  5. Oct 29, 2009 #4


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    I agree with the advice above, that if you have access to a library and/or live near a college bookstore then looking though books is the best way to find what works for you. We all learn different ways, so it is great that there is such a variety of books to chose from. IF that is just not possible, used copies of old editions of many books can be found online for cheap, so you may be able to pick up a few books without spending much.

    If you have no background, I recommend elementary linear algebra by Anton - used copies of old editions are cheap and quite good. The free online book by Hefferon is also a good choice, although at a slightly higher level than Anton - you may as well start there since it is free, and has a solution manual as well. It is professional quality, only free! I also like the Schaum outline of linear algebra.

    Axler's book that has been mentioned alread is excellent, and I have carefully worked through a lot of it, but it is not useful if you have no background in the subject, in my opinion. Even in the preface he states that the book is for a second course.

    Finally, after taking an elementary course in linear algebra, I found that I like the way Apostol presents it in Calculus volume II (volume I has some duplicate chapters on linear algebra, but volume II covers it all and shows how it is used in differential equations and multivariable calculus). It is actually in the same spirit of my notes from when I took the elementary course, although the course I took was not as advanced as Apostol. It would have been too much for me to start with, but it is written assuming you know no linear algebra and I know that many folks have learned from it in the past, so it may work for you. It is quite expensive and different than some treatmets, so I would only go this route if you can borrow it before you shell out the serious money.

    By the way, I love Strang's Linear algebra and its applications. I have had the third edition for a dozen or more years. When I took linear algebra we used no book, and did more of the abstract aspects than Strang covers, at the expense of learning nothing about matrix square roots, LU and QR decompositions, etc. I felt like Strang taught me how to use the linear algebra I knew in very practical matrix problems - the kind of problems that do come up in my work. But I agree that it would be a terrible book to learn from for the first time, and has a funny mix of topics to be used for a second course in the subject, too.

    Good luck,

  6. Oct 29, 2009 #5
    Strangs video lectures are posted on MIT OCW. Maybe they will be useful for you.
  7. Oct 29, 2009 #6
    I have a bit of the same problem, I bought Strang's book because my class using yet another, immeasurable more horrible Linear Algebra book. But Strang ain't doing it for me. I found this free PDF book from a professor at St. Michael's College, not sure what it's like but I'll be checking it out.

  8. Oct 30, 2009 #7
    For a first course, this book has no parallel. None of the other major books come close to this one. It's basically perfect, except it doesn't talk about inner product spaces which is all right but it would have been nice to learn from Hefferon.
  9. Oct 30, 2009 #8

    Gib Z

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    Can anyone else confirm this? I downloaded Hefforon's book about a year ago but put off learning linear algebra until now. I have a book called "Matrix Algebra" by Franz Hohn, it seems quite good as well. Does anyone have experiences with both books and can express strengths and weaknesses? I know linear algebra is wider than just matrix algebra, how much Wider is it? And does Hohn cover any more than just matrix algebra?
  10. Oct 30, 2009 #9
    I also liked the Hefferon book. If you need help with the basics, there are some good lecture notes here (also in pdf):


    I found Strang's OCW videos really intermittent - some of them were inspired and others were just awful.

    I haven't watched them, but there are a bunch of lectures available from UCCS:


    Add "archive.php?type=valid" to the course url to bypass registration.
    (beware, in the ones marked "MathOnline" the teacher uses an annoying computerized overhead)
  11. Nov 5, 2009 #10

    I am currently half-way through Strangs Introduction to Linear Algebra, Second Edition.
    Together with his online lectures, assignments, exams and other goodies, I feel it's a nice way to learn the subject.
    After looking through a couple of other books, I get the idea that Strangs treatment is less theoretical.
  12. Dec 14, 2009 #11

    What about this linear algebra text?

    I quit on Gilbert Strang also, I found it tedious. This book is 300 pages and I think covers everything essential with theorems, proofs and examples littering every page. I've found that the odd proof goes over my head but mainly it's the only book that, so far, has made the methods stick in my head. I'd love to hear thoughts on its quality.
  13. Dec 14, 2009 #12
    It is good for the basics (as I mentioned a couple posts ago...)

  14. Dec 14, 2009 #13
    Are we talking about lower div linear algebra? Like the kind you take in your first or second year, or are we talking about the first upper div?

    For lower division, I personally like Anton's "Elementary Linear Algebra" I guess the newer editions get a bad rap, but I have the seventh edition and I think its great. Older editions are dirt cheap too.

    For upper div, Ive been using Friedberg's "Linear Algebra" for class and Axler's "linear algebra done right" as a supplement. Axler's writing style is much more clear and vibrant than just about any math book ive read, but the book is a bit light on exercises and such. Friedbergs is a bit more rigorous than Axler's, but I think they complement each other well.
  15. Dec 26, 2009 #14


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    Hefferon's book is impressive! The book is as clear as it could possibly be, shows lots of examples and practical applications and is quite rigorous at the same time (the first proof shows up on page four!). I wish I had used it for my first LA course as an undergrad...
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