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Books (but not just any!)

  1. Dec 15, 2005 #1
    What are some good rigorous books on linear algebra?

    I am a HS senior, but I fear that college may not cover linear algebra as intensively as...well, would be preferred by a prospective pure math major (me! :redface:).
    So, what books would you suggest?
  2. jcsd
  3. Dec 16, 2005 #2
    theory or practical?

    i like my friedberg book its served me well.
  4. Dec 16, 2005 #3
    Theoretical: Sheldon Axler, Linear Algebra Done Right.
    A rigorous grounding in the theory with powerful de-emphasis of matrix methods. Without matrices, the results of the theory are very clear and intuitive. Determinants aren't even introduced (nor are they necessary) until the last chapter. There are even some cute applications in there that I haven't seen in any of those matrix theory books.
  5. Dec 16, 2005 #4


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    The best thing to do is to go to the second hand bookstore and search yourself.

    First, read the preface. That's very important because it tells you who the book is written for, and what they expect the reader to know.

    Second, take a glance at the topics. You certainly don't want a book that's filled with topics like... "Applications to...". Not that it's a bad thing, but from my experience authors do this to make math "more" fun, but it is already FUN! This usually results in a book dependent on visualization, which, in my opinion, is not the best thing for a prospective pure math student.

    Third, read some pages at the beginning, or in the middle. Try to get a feel for the book. If you don't know what the symbols are, don't let that scare you, since you will learn them as you read.

    Anyways, if it turns out to be crappy, it's no big deal because you only paid $5 for it at the second hand bookstore. :biggrin:
  6. Dec 16, 2005 #5
    (Scare me??) Hey--if I understand the symbols in the middle of the book~~>then it already is, probably, too easy :rolleyes:
  7. Dec 16, 2005 #6


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    i have written one, it is free and covers 1 or 2 semesters of collerge level lienar algebra, and is noyl 15 pages long. goto http://www.math.uga.edu/~roy/ and take class notes #1, with my compliments.
    or for a better one, goto sharipov's webpage.

    or buy hoffman and kunze, or shilov. there are lots of good books out there.

    i would be curious to know if my book has any value to anyone however. so far i have very little feedback.:smile:
    Last edited: Dec 16, 2005
  8. Dec 19, 2005 #7
  9. Dec 20, 2005 #8


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  10. Dec 22, 2005 #9


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    the first thing to learn is the meaning of linear independence. here it is:

    if R is any commutative ring with 1, and V is an abelian group allowing multiplication by elements of R, then a collection {a1,.....an,......} of elements of V is "linearly independent over R" if and only if the only equation

    c1a1+......+cmam = 0, which is true, where the a's are from the collection, nd the c's are from R, is one with all the c's equal to 0.


    1) prove the monomials, 1, x, x^2, are linearly independent over the real numbers, but not over the ring of polynomials.

    2) prove the functions 1, e^x, e^2x, are independent over the reals, but not over the ring of real valued continuous functions.

    3) prove that the real numbers {1, sqrt(2)} are linearly independent over the rationals, but not over the reals.

    4) prove that in the space of all pairs (a,b) of real numbers, there exist 2 independent pairs, but any three pairs are dependent (over the reals).

    if you can do these you will be fine.
  11. Dec 22, 2005 #10
    I would HIGHLY recommend "The Theory of Matrices" by Lancaster et. al. I'm not too sure if it's even in publication any more, but it shouldn't be too hard to get a used copy--there's one at powells.com for only $22 right now! Get it!
  12. Dec 28, 2005 #11


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    Just curious as to where you think Linear Algebra will be covered if not at a univeristy? Where do you suppose Math Majors get Linear Algebra?:confused:
  13. Dec 28, 2005 #12
    I thought linear algebra was a general math course, usually taken part of general education or other requirements, for any college major (usually in the sciences).
  14. Dec 28, 2005 #13
    I am not sure about your school, but here we have two linear algebra classes. One is applied, the other is pure. The first is taken by engineering and cs majors, the latter is taken by math and physics majors.
  15. Dec 29, 2005 #14
    You lost me there. :rofl:
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