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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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  • $\begingroup$ 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). $\endgroup$ Jul 31, 2017 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. :) $\endgroup$
    – Yes
    Jul 31, 2017 at 18:26
  • $\begingroup$ I am looking more for vector space theory $\endgroup$
    – user468462
    Jul 31, 2017 at 18:47
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    $\begingroup$ Voting to reopen because this question is about vector space theory, while the alleged dupe target is clearly application-focused. $\endgroup$ Jan 16, 2020 at 18:23

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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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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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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, 2017 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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