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I think, now is the time I should move on to do different area of mathematics. I have done real analysis and topology from Baby Rudin and James Munkres, respectively. I’m thinking to do linear algebra. I’m looking for “standard text” in linear algebra. By standard text, I mean standard text in real analysis is Baby Rudin, Tom Apostol, etc, and in topology Munkres, Dugundji etc. I have seen linear algebra done right by Axler and linear algebra by Hoffman book. IMO those book is basic to my taste. Dugundji is an amazing topology book. Is there an equivalent book in linear algebra? By equivalent I mean, in terms of rigorousness and exercise/problem in textbook.

Edit: I read almost all linear algebra book recommended by SE users. One thing is common in those books are examples and computational problems. There are lots & lots of examples(in the order of 10 in each section). Some examples involve concepts of number theory, matrix, etc. which I have never studied. I guess, I’m looking for a book which don’t contain crazy amount of examples.

user264745
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    Are you studying mathematics on your own or as a part of a college curriculum? – Miguel Jun 06 '22 at 19:58
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    Hoffman and Kunze is not basic, is it? Linear Algebra by Friedberg et al is quite standard. Linear Algebra and Its Applications. by Lax is very good and seems like the kind of book you're looking for. – littleO Jun 06 '22 at 20:06
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    There's nothing wrong with reading a basic book... Sometimes material is easy, or presented very well. That should be viewed as a positive! That said, if you want a "more advanced" book on linear algebra, you might try Knapp's Basic Algebra. It's still extremely well written, but comes off as more formal, and moves more quickly than other linear algebra books. If you want to move past that, you're getting into module theory, and you may want to look at, for instance, chapters III and VI of Aluffi's Algebra: Chapter 0. – HallaSurvivor Jun 06 '22 at 20:19
  • @littleO yeah, I agree. Saying basic, is a bold claim? I said basic because I read first two section(vector space and subspace) of chapter 2, I find thing(definition and exercise) easy/basic. Thank you so much for recommending books. – user264745 Jun 06 '22 at 20:43
  • @HallaSurvivor thank you so much for recommending book. – user264745 Jun 06 '22 at 20:50
  • Does this answer your question? Where to start learning Linear Algebra? – user1147844 Apr 23 '23 at 21:30

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The 2022 standard text for basic Linear Algebra is Gilbert Strang's Linear Algebra. It is used in a more or less direct way in every university I have ever been, and should be in every Mathematical Library which respects itself.

I would suggest you start there and there see where you should focus. It starts from ground zero, so I guess you could also replenish any shortcomings you may have acquired over your studies.

algevristis
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  • That book is more appropriate for applied perspective. – user264745 Jun 08 '22 at 11:51
  • I do not know what you mean by "applied" perspective. I have personally read it cover-to-cover as a math major and it has everything someone studying maths should know.

    All the basic lemmas, properties and theorems are there with more than good proof. I do not understand your reasoning behind "applied" perspective.

     – algevristis Jun 08 '22 at 11:53
  • By applied I meant computational. For instance, one can do integration in two ways 1)compute integral 2)study real analysis. I have done calculus, DE, linear algebra, vector calculus, etc from “applied perspective”. – user264745 Jun 08 '22 at 12:00
  • Oh now I see. Well, the computational approach is best from a mathematics-teaching standpoint. A theorem is useless if the student cannot properly apply it, that's why every introductory (and even more advanced) book has a plethora of solved and unsolved problems.

    If you have read all the books MathSE users have talked about (as you claim) then it is natural to suppose that you have a more than decent knowledge of linear algebra and as such should move on.

     – algevristis Jun 08 '22 at 12:03
  • “Read all book” don’t take that sentence out of context. In every book, author follows a pattern. PMA by Walter Rudin book is more or less kind of french school[meaning definition-theorem-proof-examples(sometime)]. Most linear algebra(including Hoffman, Axler, Friedberg) book have following pattern, definition-examples-examples-theorem. – user264745 Jun 08 '22 at 12:09
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Michael Artin’s “Algebra” contains some good stuff on the Spectral Theorems for for various types of operators as well as some intro to Lie groups, isometries of the plane, block manipulation of matrices and some other more abstract algebraic stuff relating to linear algebra if you are interested!

Kevin
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