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    $\begingroup$ Dan, it might be helpful to know what the audience for your class is. Are the students math majors or not? Have they had proof-based math already or not? In particular, some textbooks are written with the assumption that students are working with proofs for the first time and try to ease the transition; some assume students are already completely comfortable with proofs; and some don't care about proofs at all and just aim to show how to do calculations, like a typical calculus book. $\endgroup$ Commented Mar 4, 2010 at 14:47
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    $\begingroup$ Hi Mark, I think there will be a range of students, mostly non-math majors, and all of them writing proofs for the first time. I feel convinced by now that Axler would not be the right choice. $\endgroup$ Commented Mar 4, 2010 at 18:43
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    $\begingroup$ Why does no one go over applied linear algebra, or more, why is there no book that actually talks seriously about the computational end and about the theory. By computational end I mean the REAL computational end, that which is actually done on a computer or at least is the background to understand those algorithms. If there were a nice undergraduate version of Demmel then I'd defer to that book, but so far as I know such a book doesn't exist. If you're going to split linear algebra at all it would seem to be Theoretical Linear Algebra and Computational Linear Algebra $\endgroup$ Commented May 23, 2010 at 0:23
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    $\begingroup$ While I've had precisely that experience on several occasions, do you $\textit{really}$ want to be hated for the whole semester, as opposed to only the second half? The reason why many (most?) recent books start with matrices and linear systems is that at least this way students will learn something in the first half, rather than giving up early and closing their minds under the onslaught of abstraction. $\endgroup$ Commented May 23, 2010 at 1:33
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    $\begingroup$ Mainly because computational linear algebra by hand is frustrating and pointless. $\endgroup$ Commented Jun 19, 2010 at 11:14