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I took a course of Linear Algebra, but it was too basic (it only covered some elementary concepts of matrices and vectors). I am planning to purchase one of the three: Axler's Linear Algebra Done Right, Friedberg's Linear Algebra or Shilov's Linear Algebra. After one of those, I will read Hoffman's Linear Algebra, which I have learned is some advances Linear Algebra.

The topics I learned were the row echelon form, matrices operations, linear equations, inverse matrices, determinants, basic concepts of vectors, eigenvalues and eigenvectors. I want, however, to focus on the theory of it, rather than the applications (which is why I have not considered Strang's).

My Calculus course, however, has been very deep, so I consider myself able to learn proof-based mathematics books.

So, concluding, which of these three books would you recommend to me to read.

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  • $\begingroup$ If by "Hoffman's Linear Algebra" you mean Linear Algebra by Hoffman/Kunze then, in view of the fact that you've already studied some elementary linear algebra, you don't need to read anything before it. It was designed for students without prior knowledge of linear algebra, although most students studying the book will have had an elementary linear algebra course. See my answer to this question and the comments to my answer for more details. $\endgroup$ – Dave L. Renfro Sep 18 '18 at 19:23
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    $\begingroup$ Some similar/relevant (useful) posts: one, two, three, four, five. As you can see, Axler's text seems to come up a lot on this site and is a point of mild controversy. $\endgroup$ – Ben Grossmann Sep 18 '18 at 19:32
  • $\begingroup$ Consider Treil's Linear Algebra Done Wrong $\endgroup$ – vonbrand Feb 29 '20 at 14:05
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I learned from Hoffman and Kunze and taught from Axler. Both are fine books. It might interest you to note that H&K was written for a course taken by sophomore math majors, and other interested parties, at MIT. The book is somewhat sophisticated, which is a testimony to the quality of MIT students. Nonetheless, if you are comfortable with proof based courses, it would not be unreasonable, even for a first go at linear algebra. You might even consider using H&K in conjunction with Axler, to get two different perspectives on the material.

A book which I always enjoyed was Halmos' "Finite Dimensional Vector Spaces." If you are near a college or university library, you might want to have a look at it. I thought it was available through Springer, but am not sure. It could be out of print.

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  • $\begingroup$ Halmos' book is available in the Undergraduate Texts in Mathematics series from Springer. $\endgroup$ – Chris Leary Sep 18 '18 at 20:22
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I don't know the other books in detail, but I can really recommend Shilov. It is self-contained and thorough, and it's full of exercises, so quite good for self-study. It's also a Dover book, so it's affordable.

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