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[Questions about LA books are many, and I went through lot of them - hope this one is worth being asked separately]

I'm going through Strang's "Introduction to Linear Algebra" (supplement with video course) and it's pretty good and clear. My problem with it is there is zero proofs and very little rigour in general. Prof Strang explains book and course mostly for non-math majors which explain why this is so.

Learning basics from this book is fine, but I'd like to have a companion book that is rigorous and has more proofs and formals on the same basic LA subjects. Which one of the many LA books out there is good for this?

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I highly recommend Sheldon Axler's Linear Algebra Done Right. Unlike a lot of linear algebra texts, Axler's is very axiomatic and covers much of the standard material from a rigorous perspective. It's almost exclusively proof-based material, and he's very thorough without being overly pedantic. It's also not that expensive compared to many other texts.

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