Linear Algebra Book Recommendation?

In summary, Chris Maness is looking for a good reference to help him understand the difficult sections added in the 2005 edition of Mary Boas' book "Mathematical Methods in the Physical Sciences". Suggestions from other users include Serge Lang's "Introduction to Linear Algebra", Lang and Paul Shields' "Elementary Linear Algebra", Sheldon Axler's "Linear Algebra Done Right", Sergei Treil's "Linear Algebra Done Wrong", and David Lay's book. Treil's book is highly recommended for its selection of topics and practical approach, as well as its coverage of topics such as tensors and Jordan canonical form. It is also available for free.
  • #1
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I am almost finished with the LA chapter in Mary Boas' "Mathematical Methods in the Physical Sciences",. I love the book so far except for the sections in chapter three that she added in the 2005 edition. They are really difficult for me to unpack all by myself. I need a better reference since I have never taken this course. I have Gilbert Strang's book which is not as densely written, but unfortunately it does not seem to contain a section on general vector space.

Can anyone recommend a good reference to get me through this patch. Something that correlates well with Boas would be a plus as this was my first treatment on the subject.

Thanks,
Chris Maness
 
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  • #2
Have you tried checking out the textbook section of the forums? There are reviews of many linear algebra books here:

https://www.physicsforums.com/forumdisplay.php?f=21

I don't know Boas' book, but looking at the table of contents for chapter 3 on Amazon, I think you would find Serge Lang's "Introduction to Linear Algebra" to be a good choice. I don't like Strang's "Linear Algebra and Its Applications" at all - I found it to be somewhat incoherent and poorly organized. Lang is very clear and does everything on (finite dimensional) vector spaces after the first couple of motivational chapters covering vectors and matrices.
 
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  • #3
jbunniii said:
Have you tried checking out the textbook section of the forums? There are reviews of many linear algebra books here:

https://www.physicsforums.com/forumdisplay.php?f=21

I don't know Boas' book, but looking at the table of contents for chapter 3 on Amazon, I think you would find Serge Lang's "Introduction to Linear Algebra" to be a good choice. I don't like Strang's "Linear Algebra and Its Applications" at all - I found it to be somewhat incoherent and poorly organized. Lang is very clear and does everything on (finite dimensional) vector spaces after the first couple of motivational chapters covering vectors and matrices.

I second Lang.

The following book is also good and free: http://www.math.brown.edu/~treil/papers/LADW/LADW.html But it might be too difficult for now...
 
  • #4
Thanks guys. Yes, the easier the better. I just need it to the level I can understand a medium difficulty undergrad quantum mechanics class. Another friend recommended Lay. I see that opinions vary on that text.

Edit: My grad level text that I will be starting in the fall does not look that much harder than Boas, so I feel I am on the right track. She is using Arfken for a grad level methods course.

Thanks,
Chris Maness
 
  • #6
Elementary linear algebra by Serge Lang in conjunction with Paul Shields Elementary Linear Algebra. Both can be had for under 20.
 
  • #7
"Linear algebra done right" by Sheldon Axler is a good and relatively short book, with a selection of topics that's appropriate for a QM student. An often recommended alternative is "Linear algebra done wrong" by Sergei Treil. I haven't read the latter, but the table of contents looks good. There's a pdf version that you can download legally for free: http://www.math.brown.edu/~treil/papers/LADW/LADW.html.
 
  • #8
Fredrik said:
"Linear algebra done right" by Sheldon Axler is a good and relatively short book, with a selection of topics that's appropriate for a QM student. An often recommended alternative is "Linear algebra done wrong" by Sergei Treil. I haven't read the latter, but the table of contents looks good. There's a pdf version that you can download legally for free: http://www.math.brown.edu/~treil/papers/LADW/LADW.html.

I don't like Axler's book. While it has many beautiful proofs and point of views that are original, he also avoids using the determinant a lot. I think this is a shame. This makes the book only really useful for students who are very comfortable with LA already and who want another point of view. Treil's book on the other hand is a work of art. It contains everything you ever want to know about LA, and (contrary to Axler) it does it in a practical way. Very well written (but not easy).
 
  • #9
I will have to check out Treil's book.

Chris
 
  • #10
I checked out an older edition of Strang's book from my library, which has been very useful because it closely follows his lecture series on MIT Opencourseware. It's also pretty good in its own right.
 
  • #11
I can't really compare it to other linear algebra books, since I was assigned it for class, but David Lay's book is very good.
 
  • #12
I've read the first four chapters (of nine) of Treil's book now. So far it's really great, even better than I remember Axler to be. One of the things I liked about Axler is that the selection of topics is very good for a physics student, but Treil's selection is probably even better. There's even a chapter on tensors. So I think this is my new favorite linear algebra book.
 
  • #13
Fredrik said:
I've read the first four chapters (of nine) of Treil's book now. So far it's really great, even better than I remember Axler to be. One of the things I liked about Axler is that the selection of topics is very good for a physics student, but Treil's selection is probably even better. There's even a chapter on tensors. So I think this is my new favorite linear algebra book.

Yeah, it's good isn't it? I like it because it contains all the topics one should know about linear algebra. It even has discussions on stuff like condition numbers, tensors, Jordan canonical form, etc. And it does it all in the very modern language of vector spaces (which might make it unsuitable for beginning students though). But I'm really charmed by his selection of problems, they're not too difficult but they really do help understand the material. And above all: it's completely free!
 
  • #14
Here is what you need arranged in terms of excellence.

Jeffrey Holt, James Defranza& Daniel Gagliardi, Keith Nicholson, David Poole, David Lay and Gilbert Strang. The first two are excellent in terms of clarity of explanations, logical flow and proofs.

Once you have gone through any of these books, you might then move onto higher stuff but you definitely will be on point with any of these books.
 

1. What is the best linear algebra book for beginners?

The best linear algebra book for beginners is "Introduction to Linear Algebra" by Gilbert Strang. It covers all the fundamental concepts of linear algebra in an easy-to-understand manner and provides plenty of examples and exercises for practice.

2. Which linear algebra book is suitable for self-study?

"Linear Algebra Done Right" by Sheldon Axler is a great choice for self-study. It has a clear and concise writing style, and the author provides intuitive explanations and proofs for the concepts rather than focusing on abstract mathematical notation.

3. Are there any linear algebra books that focus on applications?

Yes, "Linear Algebra and Its Applications" by David Lay is a well-regarded book that focuses on the applications of linear algebra in various fields such as engineering, physics, and economics. It also includes real-world examples and exercises to help readers understand the practical applications of the concepts.

4. What is the best linear algebra book for advanced topics?

"Linear Algebra" by Serge Lang is a highly recommended book for readers who already have a strong foundation in linear algebra and want to delve into more advanced topics. It covers a wide range of topics, including abstract vector spaces, linear transformations, and spectral theory.

5. Is there a free online resource for learning linear algebra?

Yes, "Linear Algebra" by Jim Hefferon is a free online textbook that covers all the essential topics of linear algebra. It includes interactive exercises and solutions, making it a great resource for self-study or as a supplement to a traditional textbook.

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