Is Hoffman-Kunze a good book to read next?

Solution 1:

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.