Linear Algebra book supplement to Axler I have been self-studying Linear Algebra from Linear Algebra done Right by Axler for the past one month. So far I haven't encountered Matrices/solving linear equations and the book doesn't seem to talk about Matrices at all (probably until the last chapter of Trace and Determinant) 
What book should I use as a supplement to Axler ?
 A: If you're studying Linear Algebra done Right, there's a natural supplement:
Linear Algebra done Wrong, by Sergei Treil, freely available at that link. Unlike Axler, the author doesn't shy away from determinants, which I think is to its benefit.
(Also, I'm not entirely convinced that Axler doesn't talk about matrices... a matrix is just a linear transformation, represented in terms of a certain basis. It's how he proves a few theorems, IIRC...)
A: I like Kenneth Hoffman's Linear Algebra http://www.amazon.com/Linear-Algebra-Edition-Kenneth-Hoffman/dp/0135367972
A: Strang's "Introduction to Linear Algebra".
Axler does not use determinants, and Strang's book is more traditional than Axler's in that respect. So, with Strang's and Axler's textbooks he will gain spherical knowledge on the subject since he will be working on both sides.
A: I would recommend Shilov's Linear Algebra. The first chapter is actually on determinants, and a lot of the content of the book builds on them, so you could say that its approach is the opposite of Axler's. Despite this and the fact that it's somewhat of an old book, a lot of people find it equally as illuminating as Axler. Not to mention, it contains about 400 pages of material despite being $13 (Dover edition), so it's quite worth the money.
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