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    $\begingroup$ Definitely the book I would recommend for non-math majors. It has plenty of examples to motivate topics, which is what non-mathematicians need in order to be interested in linear algebra. Vector space axioms are the absolute worst way to teach linear algebra to any group of people that is not wholly composed of math majors. $\endgroup$ Commented Jun 20, 2010 at 2:13
  • $\begingroup$ If anyone is still looking for such a book, this book was rewritten as Gilbert Strang, Introduction to Linear Algebra, now in its fourth edition (as of 2016). $\endgroup$ Commented May 31, 2016 at 19:37
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    $\begingroup$ How suitable is Strang's book for mathematicians? I am not convinced. I considered it for teaching but the entire lack of formal definitions of vector spaces is really at odds with everything I believe in. $\endgroup$ Commented Jul 31, 2017 at 21:26
  • $\begingroup$ With a background in mathematical physics, signal processing for advanced imaging sensors, and combinatorics, I certainly would have benefitted greatly from a course combining a good book on linear algebra and Strang's Intoduction to Applied Mathematics. $\endgroup$ Commented Apr 3, 2018 at 13:10