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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Rodrigo de Azevedo
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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). – Sean Roberson Jul 31 '17 at 18:15
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Are you looking for a vector-space-theory-oriented linear algebra or a matrx-theory-oriented linear algebra text? Recommendations could depend on this. :) – Yes Jul 31 '17 at 18:26
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I am looking more for vector space theory – Jul 31 '17 at 18:47
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2Voting to reopen because this question is about vector space theory, while the alleged dupe target is clearly application-focused. – darij grinberg Jan 16 '20 at 18:23
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Some free sources well worth their salt (more so, I think, than many existing books):
Jim Hefferon, Linear Algebra. This is a well-known open-source textbook and has lots of good exercises.
Isaiah Lankham, Bruno Nachtergaele, Anne Schilling, Linear Algebra - As an Introduction to Abstract Mathematics. This one is less comprehensive and detailed as some might like, but it's good at what it does.
Here are some others that I haven't taken a proper look at, but suspect to be of high quality as well:
Peter J. Cameron, Notes on Linear Algebra. I haven't actually checked this one out, but I know Cameron as a good writer.
Sergei Treil, Linear Algebra Done Wrong. This one has somewhat of a geometric slant and assumes more familiarity with mathematics than the others.
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:
- Neil Strickland, Linear Mathematics with Applications. These notes are much more rigorous than the title might make you believe.
darij grinberg
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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.
Tai
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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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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.
JohnColtraneisJC
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