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    $\begingroup$ In the end, this is the book I decided to go with. $\endgroup$ Commented May 24, 2010 at 19:18
  • $\begingroup$ Mark it as the right answer, then:) This book isn't perfect, but I liked it a lot and I hope that so will you and your students. $\endgroup$ Commented May 24, 2010 at 22:22
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    $\begingroup$ Now that I'm a month into the course, I think I can heartily say that I'm happy with the book. No, it isn't perfect, but quite often the complaints I have are addressed in the author's preface for instructors (in the instructor version) and several times I've become convinced that Lay has a good point, and there's a good reason for doing things the way he does. It's very tempting to lay on tons of concepts early on in a linear algebra course. Lay's book is good about introducing concepts slowly, and then reinforcing them later with new viewpoints. $\endgroup$ Commented Sep 19, 2010 at 23:49
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    $\begingroup$ Lay has some serious flaws. He calls the dot product of two vectors in $\mathbb{R}^n$ "the inner product", as though this were the only inner product. I have gathered that this usage is common in the applied math world, but it is inappropriate in an introductory linear algebra book because you might want the students to learn the correct meaning of "inner product". The Cauchy-Schwarz Inequality is proven using projections, which is absurd, because all you need is some algebra and basic properties of inner product. The proof (using projections) is also more difficult than the usual proof. $\endgroup$ Commented Nov 2, 2013 at 0:54
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    $\begingroup$ I thought the presentation of abstract material such as subspaces and inner product spaces was weak and relied excessively on matrix algebra. I know most students who aren't math majors hate this stuff and I don't know if there is any book that will make them like it.I admit I can't recommend another book. I used Strang's book once and, to put it positively, I'll say I much preferred Lay's (the only relative advantage is that Strang does cover the matrix exponential). $\endgroup$ Commented Nov 2, 2013 at 1:04