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Hopefully this question is appropriate. Has anyone read Frank M. Stewart's, Introduction to Linear Algebra and how good of an introductory level book is it? It was published in 1963.

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  • $\begingroup$ Stewart was a good book. I preferred Howard Anton's book though :) $\endgroup$ – Ahmed Masud Jan 5 '12 at 7:45
  • $\begingroup$ @AhmedMasud: Could you be more specific? $\endgroup$ – Robert S. Barnes Jan 5 '12 at 9:47
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I actually have much experience of linear algebra self teaching (I missed all the linear algebra lectures of my first term (which was not an intro course - it was a top 2 uni [I would rather not say]). Needless to say, with one month before start of term tests, I had my work cut out.

Lecture notes were provided, but incomplete (e.g. no proofs) so I went out and bought S. Axler's Linear algebra done right (L.A.D.R).

The first four chapters were the best of any book I have read to date - layout was easy, proofs were easy and his sentences flow well. There are not any solutions to the exercises but certainly for the first 6 chapters you won't need any (the first three chapters take up a 2 mth course in many unis and reading up to 7 will be one year usually) because the questions are extremely easy (though illuminating!).

The negatives: Many people here discredit Axler - I'll admit the book is strange after chapter 5/6 though on the whole doesn't get too weird. By strange I mean some extremely non-standard approaches (i.m.o. incorrect) are put in. I had to unlearn the material in chapter 5/6 (whatever one was the eigenvalue chap.) and find a book on determinants. He doesn't treat things well in this section (his approach doesn't work well for vector spaces over R and C for instance and - obviosuly - he doesn't emphasize the minimum polynomial as much as he should).

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  • $\begingroup$ You said, "The first four chapters were the best of any book I have read to date". Exactly how many intro level Linear Algebra books have you read? $\endgroup$ – Robert S. Barnes Jan 15 '12 at 16:18
  • $\begingroup$ This wasn't really a critique of other lienar algebra books - the only other book I've read is Hoffmann and Kunze - but as a testament to the book itself; I really actually couldn't stop reading the first three chapters (the fourth is really just a short interlude) and went through them quickly. It was more like a novel than a maths text. $\endgroup$ – Adam Jan 15 '12 at 16:22
  • $\begingroup$ How did you like Hoffman and Kunze? That's the other book I happen to have laying around the house... $\endgroup$ – Robert S. Barnes Jan 15 '12 at 17:46
  • $\begingroup$ Also, the description of Axler's book on Amazon says that it's for a second course in L.A. Is that right or is it an intro level book? $\endgroup$ – Robert S. Barnes Jan 15 '12 at 17:50
  • $\begingroup$ I certainly wouldn't listen to what Amazon says - the issue comes from the annoying 'fad' of universities in the last decade to teach a matrices and vectors course where you work with 2x2 matrices or whatever is on these courses before beginning lienar algebra. Before this time the material in Axler, Kunze and so on were first exposure to lienar algebra to many students. Well I would self teach from Axler and another text because determinants are important and Axler has bizarre approaches. Howerver, Kunze is certainly more of a mathematicians book ... $\endgroup$ – Adam Jan 15 '12 at 18:03

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