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I'm planning on self-studying linear algebra, and trying to decide on a book. I'm thinking of using Hoffman and Kunze.

What sort of experience is required to handle Hoffman and Kunze?

So far, I've read most of Axler's Linear Algebra Done Right. (It was for a class in high school, so we just worked through it and got as far as we got.) I feel like I understand it pretty well, and I really liked it, but I've read that it has a rather unusual approach and I would like to try something different.

I've read that Hoffman and Kunze is good, but that it is heavy on the algebra. I'm not sure how do calibrate that, though. Does it mean "Don't use it for linear algebra for engineers" or "You should have a year of algebra, but if you have that, it's not a big deal". (I guess it's somewhere in between.)

I specifically like that it includes a strong emphasis on matrices, which are pointedly ignored in Axler, without devolving into being just a manual for computation.

This is my impression of the book from having read around (mostly here), but if something of it is wrong, please correct me. I have very little experience to provide comparison and normalize the different recommendations I've read.

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    $\begingroup$ what is your goal? there are thousands of linear algebra textbooks. do you want to read one after another? $\endgroup$
    – abel
    Commented Dec 23, 2014 at 22:43
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    $\begingroup$ H&K will mostly be review... you might like: lulu.com/us/en/shop/sergei-winitzki/… $\endgroup$
    – user155861
    Commented Dec 23, 2014 at 22:46
  • $\begingroup$ No specific goal, I just thought that Axler shouldn't be the only experience I have with linear algebra given how important and fun it is. $\endgroup$ Commented Dec 23, 2014 at 22:47
  • $\begingroup$ @wellynaught I'll look at it. $\endgroup$ Commented Dec 23, 2014 at 22:49
  • $\begingroup$ @MarJohnson: Barbeau's book is nice as well, but it will also mostly be review. You could try Roman's Advanced Linear Algebra, but if you haven't had any analysis or abstract algebra, it may be a bit tough going. $\endgroup$
    – user155861
    Commented Dec 23, 2014 at 23:49

1 Answer 1

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Hoffman & Kunze is to linear algebra what baby Rudin is to analysis. If you plan to major in mathematics or physics, you should read it, study it, and do as many exercises from it as possible. The amount of abstract algebra in H&K is minimal, and all the definitions/background is provided so that the text is self contained. So if you were fine with Axler, you'll have no issue (though the prose in H&K is significantly dryer and more demanding than the conversational Axler, and may take some getting used to).

The reason why Axler's approach is "unusual" is that he doesn't use determinants in his presentation of eigenvalues, etc. This is nice in theory and provides alternative proofs which can be illuminating, but ultimately the approach limits one's ability to perform concrete calculations. Also, determinants cannot be banished forever in linear algebra, so at some point you need to learn about them, and the chapter in H&K covering them is excellent (though probably the most technically difficult chapter in the text). Other than that, it's all basically standard fare and the level of difficulty is comparable to H&K, though H&K covers quite a bit more than Axler.

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    $\begingroup$ That's mostly the impression I had about Axler, good to see it in writing. I'm assuming I can read "Covers quite a bit more" as "would still be interesting to read"? $\endgroup$ Commented Dec 23, 2014 at 22:51
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    $\begingroup$ "Covers quite a bit more" as in there are multiple topics and extensions of covered topics presented in H&K that are not available in Axler's presentation of the subject. The most noteworthy are systems of linear equations, determinants and multilinear forms. $\endgroup$
    – Sargera
    Commented Dec 23, 2014 at 23:49
  • $\begingroup$ Alright, sounds good. $\endgroup$ Commented Dec 23, 2014 at 23:51
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    $\begingroup$ I agree with this post. I'd like to add that I read much of the book myself as an undergrad and the only disappointing part of this book is that it has fewer examples than I would have liked. For instance, I would have enjoyed more worked examples on actually finding the Jordan normal form. In this sense I believe the book falls short. $\endgroup$
    – user2055
    Commented Dec 24, 2014 at 20:35

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