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Help decide between this books [linear algebra]

  1. Sep 25, 2013 #1
    this is for a first course in LA,can I ask the avid readers :Which teaches more of the theory and meanings Please?Which is better?:
    Introduction to Linear algebra and linear algebra by serge lang?
    Linear algebra by Shilov?
    Halmos P. R Linear Algebra Problem Book ?
    Last edited: Sep 25, 2013
  2. jcsd
  3. Sep 26, 2013 #2


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    For a first course, I think Lang's "Introduction to Linear Algebra" would be the best choice out of the ones listed (and offhand, I can't name a better introduction). His "Linear Algebra" would be a good sequel, but it assumes you have already learned the basics.

    The Shilov book is also nice but would be hard for a first exposure - if I recall correctly, the very first chapter is on determinants.

    I don't know Halmos' problem book, but I assume it is a companion for his linear algebra book, "Finite-Dimensional Vector Spaces." That's also a good book, but again it assumes you already know the equivalent of the first Lang book.

    I think you would do well to learn from the two Lang books, in the order you listed.
  4. Oct 3, 2013 #3


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    lang's books are very clkear on the ideas, short on examplkes and problms. he also does not proof read his books carefully for errors, not take great pains with topics that need careful discussion. his strength is a quick clear summary of the main ideas, and sometimes he makes something seem easy in theory that others make look hard.

    but shilov is a masterful, carefully written correct treatment of a large part of linear algebra.

    so lang may be better for a quick first pass over the material but i think in the long run shilov offers far more.

    halmos' linear algebra book, is a very expert discussion of the theory again with as i recall almost no examples or problems. I cannot imagine a beginner learning first from halmos, although i myself like the book very much for its insights.

    for a first course i would probably not choose any of these books but rather a thorough, patient introduction with examples, such as the book by paul shields, or insel, friedberg, and spence, or one of the many free books online.

    of course it depends partly on how sophisticated you are and whether you are a math major.

    there are also several free books on my website, but not so carefully written as those above.

    i also like :"linear algebra done wrong" probably for a second course, free from sergei treil's website at brown.

    http://www.math.brown.edu/~treil/papers/LADW/LADW.pdf [Broken]

    but in the end all the books you listed are good, except as noted above halmos problem book is not really a textbook.

    by now of course you are in some sense just wasting time asking, and should be actually looking at the books yourself. if money is your worry look in a library.
    Last edited by a moderator: May 6, 2017
  5. Oct 4, 2013 #4
    Thanks I've bought Shilov and old copies of lang's books.
  6. Dec 13, 2013 #5
    How did that work out for you? After 3 months my copy of Shilov still looks nearly new.
  7. Dec 14, 2013 #6
    Shilov's book is really good,but somewhat dry.
  8. Dec 14, 2013 #7
    I found it procedural and lacking explanation for the maneuvers he attempts to convey. Perhaps if I went further in?

    Let's try this, what is your favorite part(s) of the book?
  9. Dec 14, 2013 #8
    the chapter on canonical forms is pretty good,and I found some good exercices throughout the book.Also the last chapters are somewhat abstract but excellent.
  10. Dec 14, 2013 #9
    Considering the cover I wouldn't be surprised if this is one Shilov's more well developed sections. I'll give it another shot, is there anything in particular (in this section) you found particularly enlightening?
  11. Dec 14, 2013 #10
    Nothing in particular but the problem some people have with this book as whole is that it's badly translated(some say),I remember it took me a while to get through that section then I give up and looked elsewhere,and used it now and then.
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