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Linear Algebra Textbook

  1. Feb 10, 2005 #1
    Would anyone be able to recommend an excellent linear algebra textbook that you could essentially teach yourself from?

    Unfortunately I have a grad student who is more concerned with getting his Phd than helping the students.
     
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  3. Feb 10, 2005 #2

    mathwonk

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  4. Feb 21, 2005 #3
  5. May 7, 2008 #4
    The site boom.ru is OFF (I hope it is temporarily off). You are invited to visit a new site for free textbooks:

    http://freetextbooks.narod.ru.
     
  6. May 23, 2008 #5
    I find the Schaum Series books pretty useful. The linear algebra boook by Lipschituz in this series is excellent. A less rigorous book but easy to understand is 'Elementary Linear Algebra' by Anton and Rorres. I don't know about the above free books but generally I prefer a hardcopy bounded book published by well known publisher because it has been reviewed and checked for accuracy.
     
  7. May 23, 2008 #6

    mathwonk

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    both ruslan sharipov the author and i are professional mathematicians. he is no doubt too modest to respond, but you may take my objective word for it that the book recommended above is at least as high in quality as the average hard bound published book, and i think considerably higher in quality than a typical schaums book, although those are often decent if minimal in quality.

    i did not recommend it without at least reading parts of it and perusing the rest, although i do not recall if i scanned it as thoroughly as i would have done for an official review. i believe you will want to supplement it with exercises from some other source such as schaum's.
     
    Last edited: May 23, 2008
  8. May 23, 2008 #7

    mathwonk

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    ok i looked more closely at sharipov's book and i may have found a small misprint on page 74, after equation 5.5, where apparently the statement f(vi-1) = vi, should say f(vi) = vi-1.

    if that sort of thing bothers you, there may be a few more. there are also some small instances of English usage sounding odd to a native ear.

    i recommend it to you for the quality of the mathematics, the care with which the proofs are written, and the clarity of the explanations.

    in particular, the clear focus on nilpotent operators makes it much easier to understand jordan form than is often the case in most books, including my own.

    the first chapter also starts with helpful material on functions which is usually assumed, but often needed by beginners.

    i just checked on amazon for the schaums book and found that they key lemma on structure of nilpotent operators seems left as a problem for the reader. so sharipov is perhaps much more complete than schaums.

    but schaums moves much more slowly, taking hundreds of pages to do what sharipov does in under a hundred.
     
    Last edited: May 23, 2008
  9. May 23, 2008 #8
    Strang's book Linear Algebra and its Applications is considered good for learning linear algebra, and strikes me as good for self-study. Also, as he's an MIT prof, you can watch free videos of him lecturing on linear algebra over the web. The downside of it is that, like many introductory texts, the proofs are often less-than-fully-rigorous. So, it kind of depends on your purposes in learning linear algebra; if you're a math major, it's probably better to go directly to a more rigorous text, but if you're a science or engineering major, Strang is probably a good bet.
     
  10. May 23, 2008 #9

    mathwonk

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    i know everyone likes strang's books but i am not convinced. his videoed lectures reveal that he is not even close to our best lecturers at georgia, mit professor or not. still those good georgia lecturers also praise him.

    but i am just blabbing, go look at them yourself and if you like them by all means watch them. he is extremely generous to make them available for free, and he is clear. i just don't agree with the relatively low level of rigor and depth he aspires to give his audience in his explanations.
     
    Last edited: May 23, 2008
  11. May 24, 2008 #10
    It does not matter whether a book is written by MIT professor or Fields Medal winner. Does it explain things so that you as a student understand without going through so many other references. The book by Strang is good for numerical examples in linear algebra but if you want rigour and depth then this is not a book I would recommend. However it is useful book for engineers and scientist with a number of applications.
     
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