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I'm looking for some (or one) good book(s) that teach linear algebra either purely coordinate-free or ones that present the standard bag-of-tools alongside coordinate-free alternatives or discussions. Thanks!

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    $\begingroup$ I very much enjoy "A Second Course in Linear Algebra" by Brown. $\endgroup$ – Alex Youcis Jul 10 '14 at 6:19
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Stephen Roman's Advanced Linear Algebra. It's a gem.

You may also care to look at chapters 10-12 of Dummit and Foote's Abstract Algebra.

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    $\begingroup$ Thanks! These two sources are certainly along the lines of what I was looking for (and "A second course in linear algebra" is also very good). $\endgroup$ – Ittay Weiss Jul 10 '14 at 10:51
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S. Winitzki, Linear Algebra via Exterior Products (free book, coordinate-free approach)

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