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I know, that there are a similar topics of my question, but I didn't find the answer.)

$\textbf{Problem:}$ I need a book of LA for self-study, but I want to find the book like "Introduction to real analysis by G. Bartle, R. Sherbert" in analysis, but for LA. So I mean, it has to start from basic things, but with rigorous proofs and be PURE mathematical.

$\textbf{What I tried:}$ I chosed 3 books, which I found on this forum:

  1. Linear Algebra Done Right by Sheldon Axler
  2. Linear Algebra. A Modern Introduction" by David Poole
  3. Linear Algebra and Its Applications, 4th Edition by Gilbert Strang.

I started with the first one and I didn't like it, because this book is not precise as for me. ( In the first chapter author says: we will use $F$ for field, but it's ok, if u don't know, what field is, because if we write $F$, we mean $\mathbb R$ or $\mathbb C$ instead of define the field. I don't find it good. So can somebody recommend the book from my list or maybe book, that u like and looks like what I look for) Thank you in advance

mathguruu
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  • Friedberg Insel and Spence fits the bill in my opinion. – Irving Rabin Nov 23 '22 at 00:48
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    What are you hoping to get out of your linear algebra study? Axler is indeed a good choice if you're hoping to see the theory of real/complex vector spaces established rigorously. If you're really hoping to see linear algebra over more general fields, then you might need to study some abstract algebra first (groups, then fields). If the problem is purely aesthetic (in that you don't like the way Axler brushes over the term), then my advice would be to stick with it, as Axler's proofs and constructions are rigorous and often elegant. – Theo Bendit Nov 23 '22 at 00:56
  • @TheoBendit thank you, can you recommend books for abstract algebra ? – mathguruu Nov 23 '22 at 01:03
  • @AndreyYanyuk Thank u! – mathguruu Nov 23 '22 at 01:03
  • @mathguruu I'm not really widely-versed enough to do so. I was raised on Fraleigh's book, and it seemed fine enough: simple, yet perfectly rigorous. Someone discusses it in comparison with the standard by Dummit and Foote here. – Theo Bendit Nov 23 '22 at 01:18
  • because this book is not precise as for me --- I find it a bit revealing that your explanation of why it is not precise seems to indicate a misunderstanding of what "precise" means. That said, maybe some of the more advanced books listed in this answer will be suitable for you. – Dave L. Renfro Nov 23 '22 at 01:33
  • Some of the older texts might fit the bill, such as Lang, or Hoffman and Kunze, or O'Nan. – Gerry Myerson Nov 23 '22 at 01:59
  • Does this answer your question? Best Books to learn Proof-Based Linear Algebra and Matrices – user1147844 Apr 23 '23 at 21:25

2 Answers2

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Halmos' Finite Dimensional Vector Spaces or Roman's Advanced Linear Algebra are both worth considering.

wgabrielong
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Hoffman and Kunze - Linear Algebra.

Give it a try.

Diego Z.
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