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This question already has an answer here:

I have been wanting to learn about linear algebra (specifically about vector spaces) for a long time, but I am not sure what book to buy, any suggestions?

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marked as duplicate by Zain Patel, Namaste abstract-algebra Aug 1 '17 at 0:15

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Axler's Linear Algebra Done Right is a good text on linear mappings and vector spaces without being bogged down by determinants (banished to the end of the text). $\endgroup$ – Sean Roberson Jul 31 '17 at 18:15
  • $\begingroup$ Are you looking for a vector-space-theory-oriented linear algebra or a matrx-theory-oriented linear algebra text? Recommendations could depend on this. :) $\endgroup$ – Megadeth Jul 31 '17 at 18:26
  • $\begingroup$ I am looking more for vector space theory $\endgroup$ – user468462 Jul 31 '17 at 18:47
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A standard book for a first course in linear algebra is Gilbert Strang's Linear Algebra and Its Applications. After getting an initial exposure, Sheldon Axler's Linear Algebra Done Right is a good book for getting a more abstract view of linear algebra (at Carnegie Mellon, this is used for a second course in linear algebra). Finally, if you want a very abstract view of linear algebra in relation to other algebraic structures such as fields and modules, you can read the relevant portions of the legendary Abstract Algebra by Dummit and Foote.

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Some free sources well worth their salt (more so, I think, than many existing books):

Here are some others that I haven't taken a proper look at, but suspect to be of high quality as well:

All of the above cover vector spaces. As far as linear algebra without abstract vector spaces (i.e., "matrix algebra") is concerned, I can highly recommend the following:

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I think linear algebra by Hoffman and Kunze and linear algebra by Serge Lang are great books.

Also, MIT ocw has a very good online linear algebra course (including assignments, but you would need Strang's book for doing those):

https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/index.htm

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  • $\begingroup$ Serge Lang's book is terse but very widely used. $\endgroup$ – nurdyguy Jul 31 '17 at 22:24
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Differential Equations and Linear Algebra (Third Edition) by Stephen W. Goode and Scott A. Annin is a good textbook, as is Abstract Algebra by Dummit and Foote, and Linear Algebra by Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence.

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