What are the best linear algebra textbooks for self-study?

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Discussion Overview

The discussion revolves around recommendations for linear algebra textbooks suitable for self-study, particularly for graduate students seeking a theoretical approach. Participants share their experiences and preferences regarding various texts, considering factors such as depth, clarity, and the balance between theory and computation.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant expresses a need for a theoretical linear algebra book that minimizes computational content, mentioning their current selections: Friedberg, Insel, Spence; Hoffman, Kunze; and Golan.
  • Another participant critiques the Hoffman & Kunze book as overrated, describing it as dry and limited, while recommending Halmos's "Finite-Dimensional Vector Spaces" for its concise coverage.
  • Several participants suggest "Linear Algebra Done Right" by Axler for its clarity and avoidance of determinants, while noting its focus on finite-dimensional vector spaces.
  • Shilov's book is praised for its value and general coverage, though some participants mention it may be challenging to read.
  • Peter Lax's book is recommended for its rigorous approach tailored to graduate students needing a solid foundation in linear algebra.
  • One participant shares additional resources, including free materials from their website, although they note limited engagement with these notes.
  • There is mention of a desire for a table of contents from Shilov's book to aid in decision-making.

Areas of Agreement / Disagreement

Participants express a range of opinions on the recommended textbooks, with some agreeing on the merits of specific books like Shilov and Axler, while others have differing views on the effectiveness of Hoffman & Kunze. The discussion reflects multiple competing perspectives without a clear consensus on the best choice.

Contextual Notes

Participants highlight the importance of clarity and depth in the recommended texts, with some noting that certain books may be more suitable for readers with a background in rigorous mathematics. There are also references to the challenges of balancing theoretical understanding with computational skills in linear algebra.

Who May Find This Useful

This discussion may be useful for graduate students in mathematics or related fields seeking self-study resources in linear algebra, particularly those interested in theoretical approaches.

dmuthuk
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Hi, I'm a grad student in pure math and I'm trying to re-learn my linear algebra from scratch because I never learned it properly while I was an undergrad. Actually, the course I took in second year was aimed mostly at science students and so we never went into much depth (half the course was on matrix algebra). Now, I'm having trouble picking a suitable linear algebra book for self-study. I'm looking for an approach which is very theoretical and directed to a mature audience but also self-contained at the same time to some extent. I want to avoid computations and applications as much as possible, but I'm finding out that you can't learn linear algebra without getting into matrices and determinants. I was wondering if someone can suggest a few books for me. I have the following books right now:

1. Linear Algebra (4th Edition) by Friedberg, Insel, Spence
2. Linear Algebra (2nd Edition) by Hoffman, Kunze
3. The Linear Algebra a Beginning Graduate Student Ought to Know by Jonathan Golan

Are these books good? I've heard a lot about the Hoffman & Kunze book. I found the Golan book by searching randomly.
 
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Be open minded. Trying to avoid all matricies can be as bad as those that try to avoid all proofs.

Linear Algebra by Kenneth M Hoffman and Ray Kunze
This is the only one on your list I am familar with. It is on all those lists of books that have Rudin and Ahfors on them. Like many other books on such lists I think this one is overrated. You can learn good stuff from it for sure, but it is dry, not that clear, covers only the minimum, and not all that general. Really expensive.
Finite-Dimensional Vector Spaces by P.R. Halmos
If you want a book that covers minimal material well and has stood the test of time this is the one. As the title implies this limits itself mostly to Finite-Dimensional Vector Spaces.
Linear Algebra Done Right by Sheldon Axler
This book is very basic and short. It is well written and avoids determinants. Limits itself mostly to Finite-Dimensional Vector Spaces.
Linear Algebra by Georgi E. Shilov
The best goodness:price book I know. Uses determinants often. Is more general and covers more material than Axler.
Advanced Linear Algebra (Graduate Texts in Mathematics) by Steven Roman
One of few basic books that covers modules. Nice topics like convexity, affine geometry, tensor products, and umbral calculus. Logically complete, but covers basic material rapidly. Many errors in 2nt edition 3rd out now
http://www.romanpress.com/MBOOKS/MathAdvLA.htm
Introduction to Linear Algebra (Undergraduate Texts in Mathematics) by Serge Lang
Nice is you like Langs style. This one can probably be skipped, but the sequel does not repeat its whole contents so both are needed for completeness.
Linear Algebra (Undergraduate Texts in Mathematics) by Serge Lang
Matrix Analysis by Roger A. Horn and Charles R. Johnson
Mabe abit more applied than you would like, but full of good stuff.
 
Linear Algebra by Curtis...I think it's not that great
The one by friedberg I liked.
 
I was in exactly the same situation as you and the book that satisfied me the most was

Linear Algebra - Peter Lax.

The author states in the Preface that this book was written for starting graduate students who needed to re-start Linear Algebra with a more rigorous approach than the one of most undergraduate courses. The book is concise, well organized and short. It is clear that Lax wrote it having in mind a reader already used to rigorous Mathematics.
 
I like lurflurf's list (I especially agree about shilov) and wish to add two freebies, the book by sharipov on his website and my notes for math 4050, and math 8000, and math 844 on my website. I also have a 4th one there: revised linear algebra notes in 15 pages, but almost no one seems to have tried to read it.
 
A lot of people say that Shilov is hard to read, but if you're a grad student you should be fine. I bought a copy of the book for about $12 on Amazon. If you want me to post up the table of contents, just let me know!
 
Thanks guys! I'll browse through these books and see which one will work out for me.
 
My geocoities.com/r-sharipov site is now off. Use the following sites instead:
http://ruslan-sharipov.ucoz.com"
http://freetextbooks.narod.ru"
 
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