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What is the best book for linear algebra?

  1. Nov 10, 2012 #1


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    I want to beginning learning linear algebra. I will be studying it on my own, so I was wondering what the best book would be.
  2. jcsd
  3. Nov 10, 2012 #2
    Depends on you. There is no objective best book, there are only book which you like or dislike.

    Anyway, what kind of math do you know already?? Are you familiar with matrices and determinants?? Are you familiar with proofs?? "Analytic" geometry?? Abstract algebra?? Are you wanting to be a physicist or a mathematician?? etc.
  4. Nov 10, 2012 #3


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    I want to be a physicist. I am familiar with proofs, although only basic geometry proofs (high school stuff). By analytic geometry I assume you mean coordinate geometry, so yes I am familiar with it. I am not familiar with matrices or determinants or abstract algebra. I have done Calculus 1 on my own and some of Calculus 2.
  5. Nov 10, 2012 #4
    One good question would be:

    Do you want a computational emphasis on linear algebra?

    Or a more theoretical approach? (Which requires proficiency in proof writing and logical reasoning)

    Usually, the proof based course covers the computational side in sufficient detail. Think of the theoretical side as making all the formulas and algorithms in the computational linear algebra course legitimate.
  6. Nov 10, 2012 #5


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    Well I am sure I would enjoy a theoretical approach more, but I think a more computational emphasis would be better for me. The reason I am self studying all of these topics is so that when I get into university I will already have a decent understanding of the topics.
  7. Nov 11, 2012 #6


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    While I do recommend getting familar with things before the course, I would also not recommend doing too much before a course starts unless the course is really demanding, covers a lot of stuff, and goes very quickly.

    The reason is simple: if you learn everything before the course starts and then go in, you will get very bored very quickly.

    The thing is that you need to understand what the expectations are of the teachers giving it, and most teachers will not expect that their students have done a lot of study on the subject which means that they will make things really basic and spend more time teaching the material to people as if they were expecting that this is all new and unfamiliar to the students (and for the majority it should be).

    If you haven't started university, then I would bet that your first classes won't be too heavy in terms of expectations relative to later years: I'm not saying they won't be serious, but I am saying that universities know that the transition to university life, particularly for subjects like physics, mathematics, engineering, computer science, and similar kinds of subjects will be daunting.

    I don't know your situation, your level of understanding and knowledge, or your aptitude, but I can say that if you spend too much time learning stuff before you start the class, then you will be absolutely bored out of your brain and it may have negative consequences for your grades and also for your attitude of the subject in a detrimental way.

    So prepare by all means, but don't end up doing the course (or too much of it) before the course actually starts.
  8. Nov 11, 2012 #7


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    chiro, the reason I am doing this all is to prepare myself, but also because I am bored to death in high school. I must assure you that your concerns of my boredom in later years affecting my grades will not be a problem. Very few things can come between me and my grades.
    But that is beside the point. Thank you for your concern, but I really just want a book recommendation.
  9. Nov 11, 2012 #8
    For my style of learning the best book has been Poole's Linear Algebra. It's very visual and intuitive in terms of introducing the topics. I don't learn well when the generalizations happen at the start and that's exactly what he avoids in his book. He starts with a simple case and then moves onto making it more abstract and general.

    I have Axler's book also which is very rigorous in comparison and I couldn't follow anything when I first got it. After getting through most of Poole's book I can understand much more of what Axler is saying because I have a simple picture of all the concepts. If you can learn from generalizations and abstractions from the start then get a book like Axler's, otherwise get Poole's. Some of my friends do actually learn starting with abstractions but I certainly don't.
  10. Nov 12, 2012 #9
    Last edited by a moderator: May 6, 2017
  11. Nov 12, 2012 #10
    Shilov is an excellent book!! But are you sure it is suitable for somebody who doesn't know anything about matrices??
    Last edited by a moderator: May 6, 2017
  12. Nov 12, 2012 #11
    Good point. I am definitely not sure whether it is suitable for someone still in high school who does not know about matrices. But its a Dover book, so it is cheap :) At least, it would be great alongside another book that is more elementary. In the worst case scenario, if it is too hard, you can put it on the shelf and take it down again when you are ready.
  13. Nov 12, 2012 #12
    Best book would be Matrix Analysis and Applied Linear Algebra Book by Carl Meyer's. The author has even put it out for free as a pdf file with the entire solutions manual on his website.
  14. Nov 12, 2012 #13


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    Due to these comments I have looked into matrices. I know how to add, subtract and find their inverses, as well as how to solve system of equations and vector combination problems. Not to say that I know a lot about matrices, but I at least know some of the basics.
  15. Nov 12, 2012 #14
    It sounds like you are pretty motivated. Any book that you can learn the basics from should be fine. Halo's recommendation is available online so that would be a good place to start. As the author states in the preface, it is tilted toward computational applications. If you get into the middle of it and then want more proofs, you could easily supplement it with a book more oriented toward the basic theory such as Shilov, Hoffman/Kunze, Axler, or Lang. (I am suspicious Axler because he put "done right" in his title.)
    Last edited: Nov 12, 2012
  16. Nov 17, 2012 #15
  17. Nov 20, 2012 #16


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