Reddit mentions of Linear Algebra and Its Applications, 3rd Edition

Gilbert Stang Linear Algebra Third Edition optical illusion is my favorite.

https://www.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0155510053/ref=sr_1_1?s=books&ie=UTF8&qid=1492964393&sr=1-1&keywords=gilbert+strang+3rd+edition

Strang's course is a great introduction. I feel that his explanations provide great intuition into how and why certain methods in linear algebra work.

Here is a link to the OCW course page: http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm

And the book website: http://math.mit.edu/~gs/linearalgebra/

By the way, used copies of previous editions of the book can be obtained at a significant discount: http://www.amazon.com/Linear-Algebra-Its-Applications-3rd/dp/0155510053/ref=sr_1_4?s=books&ie=UTF8&qid=1459432805&sr=1-4&keywords=Introduction+to+Linear+Algebra%2C+Third+Edition

While I agree with your comments on the importance of the conceptual side of linear algebra, I really don't like Axler's book. It reads, to me, as `here is the only perspective to take on this issue, read my proof and that is all.' So, you might augment it with something like Gil Strang's Linear Algebra and Its Applications.