Top Linear Algebra Texts for Advanced Courses: Reviews and Recommendations

[dijkarte]

Almost half of it's content is online? And expensive? Are you kidding me?

http://www.amazon.com/dp/1133110878/?tag=pfamazon01-20

Anyway I'm considering an advanced course in linear algebra, and after researching the library and online reviews I found these 3 texts to be the most famous ones:

http://www.amazon.com/dp/0132296543/?tag=pfamazon01-20

http://www.amazon.com/dp/0387982582/?tag=pfamazon01-20

And this graduate text:

http://www.amazon.com/dp/0486469085/?tag=pfamazon01-20

 

[intwo]

Most courses on "advanced" linear algebra are just linear algebra in a rigorous context. If you've already had a course on linear algebra, go with Linear Algebra Done Right by Axler or Linear Algebra by Hoffman and Kunze. I prefer the book by Hoffman and Kunze because it takes a traditional approach - it builds up the theory in a sequence similar to introductory linear algebra textbooks. However, Axler's non-determinant approach provides a useful perspective so you should probably just get both.

 

[dijkarte]

I've taken a comprehensive course using an older edition of Kolman's. But is not Hoffman and Kunze a quite expensive for a dated book? Unless it has a more comprehensive content than others, which I doubt telling from the number of pages...I would consider buying something newer.

What about the Dover's book? Is it rigorous as the ones you suggested?

Thanks.

 

[wisvuze]

The hoffman and kunze book is pretty old, but the material is not dated at all. I agree with intwo's suggestions, Axler's book is good as well.

http://www.amazon.com/dp/0486469085/?tag=pfamazon01-20

this one isn't really a graduate text. It is used in some first year linear algebra courses at my school, Hoffman and Kunze is probably more "advanced"

 

[dijkarte]

Anyone tried this:

http://www.amazon.com/dp/0387728287/?tag=pfamazon01-20

 

[wisvuze]

Yes, that book is very good. It is more advanced than any book mentioned so far on this thread though

 

[micromass]

Anyone tried this:

http://www.amazon.com/dp/0387728287/?tag=pfamazon01-20

Uuuh, I suggest you not to try this book yet until you have some more knowledge of linear and abstract algebra...

The Hoffman and Kunze book is very good. It is NOT outdated at all. If you want a rigorous linear algebra book, then that is the book for you.

Lang's linear algebra is also extremely good. It's quite rigorous, like all of Lang's books.

For some weird reason, I don't like Axler. He doesn't do determinants (except a weird approach in the last chapters), which I think is a mistake. Other people love the book though, so you might like it.

 

[intwo]

I've taken a comprehensive course using an older edition of Kolman's. But is not Hoffman and Kunze a quite expensive for a dated book? Unless it has a more comprehensive content than others, which I doubt telling from the number of pages...I would consider buying something newer.

What about the Dover's book? Is it rigorous as the ones you suggested?

Thanks.

It's older, but it's definitely not outdated. The books that I listed here (and the one in your differential equations thread) are very complete in a sense that they build the theory up from where most rigorous approaches to calculus left off. I think that this approach is important because it emphasizes the connection between the topics. I took calculus, differential equations, and linear algebra using standard undergraduate textbooks - the ones that produce new editions every year - but I did not realize their relations until I relearned them in a rigorous (theoretical) context.

Also, the number of pages, age, and price of a book does not typically indicate the value of the content. You might spend more money on the textbook by Hoffman and Kunze, but I guarantee that you'll spend more time on each page than most other linear algebra books. The book is dense - it's definition, theorem, proof, corollary all the way through, so you'll probably be spending a lot of time testing the theorems, providing counterexamples, thinking through the problems, etc.

For some weird reason, I don't like Axler. He doesn't do determinants (except a weird approach in the last chapters), which I think is a mistake. Other people love the book though, so you might like it.

Yeah, lots of schools use it as a main text for their advanced or theoretical linear algebra courses, but I think that Hoffman and Kunze would be more suitable. I don't think that Axler should be disregarded though; I think it should be read after Hoffman and Kunze as a "hey, you can also learn linear algebra like this!" sort of text. It's not necessary, but it could be interesting or valuable depending on your tastes. :)

 

[Sankaku]

Friedberg-Insel-Spence is a really solid intermediate-level Linear Algebra text as well. It is a bit more readable than Hoffman & Kunze. The only drawback is that it is just as stupidly expensive.
https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20

Micromass gives a nice summary of the different LA books here:
https://www.physicsforums.com/blog.php?b=3206

For the books I have read, I think those reviews are pretty spot-on...
...except that I like Axler more :-)

 

[dijkarte]

Well sounds a very good review...

The problem many universities use other texts, such as Kolman's or Howard's Elementary Linear Algebra. I've both but they are not abstract enough focusing mainly on R^n vector spaces...

I'm tempted now to try Friedberg's and probably Kunze if I can find a cheaper copy. :)