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It really depends on what you’d like to learn LA for, and how comfortable you are with abstraction: LA can span from concrete multiplication of matrices and vectors all the way to very abstract (e.g. vector spaces over general fields or even modules over rings). I know many people recommend Gilbert Strang’s introductory linear algebra (I have not read it, but it seems to fall into the former camp), but I might also recommend Sheldon Axlers Linear Algebra Done Right. In all honesty, I learned La the best from David Griffiths quantum mechanics text, although it is not a comprehensive in its coverage of the subject (not that it should be, given that it is a physics text). I guess I am trying to say that there are many different flavors and interpretations of linear algebra, and while matrices and vectors may be simple at first, it does tend to rob the subject of its richness and depth (e.g. what do these matrices represent, what are the canonical structures etc.) so I am a bit biased towards going full generality at first, and perhaps reading a more rote computation book on the side (I understand we all have limited time though).


Strang’s latest book is very much in the abstract camp, but very practical. A physicist’s linear algebra book.

https://math.mit.edu/~gs/everyone/




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