Seeking Recommendation on Linear Algebra Textbooks

[bacte2013]

Dear Physics Forum personnel,

I am a college sophomore in U.S. with a major in mathematics and an aspiring algebraic number theorist. I wrote this email to seek a recommendation on one or two outstanding linear algebra textbook that can supplement the Linear Algebra (Friedberg et al.), which is a required textbook for my theoretical linear algebra course for Fall 2015. I always enjoy studying from multiple textbooks so it would be nice for me to purchase one or two more LA books to supplement my main textbook. Ones that I currently have in mind are Hoffman/Kunze, Axler, Serge Lang, Anton, etc. but I am clueless of their contents. Could you recommend one or two LA textbooks that I can use in accordance with Friedberg?

PK

 

[jtbell]

While you're waiting for responses, you might try using the forum search feature (top right of the page) to search for the word "linear", ticking the boxes "Search titles only" and "Search this forum only". I've moved this thread to the textbooks forum, so most of the search results will be about linear algebra textbooks. Good luck!

 

[ELB27]

I would recommend Sergei Treil's "Linear Algebra Done Wrong" which you can find in full here free of charge in pdf format. It is quite rigorous and thorough, and according to some knowledgeable members of this forum contains everything you need to know about the topic. I am self-studying from it myself and can personally vouch for its quality.

 

[MidgetDwarf]

Anton Txt is wordy, hand wavy, and sometimes the examples are not fully worked. I would advice against. There is a pdf of anton floating around the web. You can download it to see if you like it.

 

[bacte2013]

I am considering one from Hoffman/Kunze, Lang, and Axler to supplement Friedberg. I taken a look at Anton and Treil, but I honestly did not like them much...

 

[verty]

Some more books for you to consider:

https://www.amazon.com/dp/0486780554/?tag=pfamazon01-20

This one should be more or less equivalent to Friedberg, it looks decent to me. If you're considering Axler, this one looks to be a good substitute.

https://www.amazon.com/dp/B00CWR4Y9M/?tag=pfamazon01-20

This one is in the old style which I like. It should be good if only because it is constructive rather than axiomatic.

---------------------------

Something different now. Looking at Amazon's Hoffman & Kunze reviews, I see the following in one of the reviews:

One problem that I see with this book is that it focuses a little too much on matrix representation of everything. While matrices certainly do have their uses in computations, it is quite possible for students to learn to rely so much on matrices that they are unable/uncomfortable with the properties that linear transformations have in of themselves.

I don't know this book but I have to object most strongly to this claim. Probably I should give reasons why but there is this thing called the burden of proof: if one makes a ridiculous claim, it is for the claimant to back it up or substantiate it. In this case, the ridiculous claim is that knowing too much about matrices is bad. I simply reject that out of hand.

This actually makes me think Hoffman & Kunze would be a good choice. I think I would choose it out of your three listed options.

 

[Fredrik]

I am considering one from Hoffman/Kunze, Lang, and Axler to supplement Friedberg. I taken a look at Anton and Treil, but I honestly did not like them much...

Since you're looking for a supplement rather than something to teach you stuff you've never seen before, I think Axler is a very good choice. But I think any of these books will do. I like Treil the best myself. It's certainly the cheapest. If you choose Axler, I still recommend that you read the stuff on determinants in Treil.

I think Anton is brilliant in many ways. That book makes almost everything easy to understand. If there's a proof you don't understand in one of the other books, you will probably understand the proof in Anton. But I still don't like the book, because I find it absurd to introduce linear transformations so late in the game (several hundred pages into the book).

 

[bacte2013]

Thank you very much for all of your advices! I actually bought Hoffman/Kunze as it was sold in special discount and I bought the brand-new U.S. Edition by $55.00! my plan is to read Friedberg as a main text and Hoffman as a supplementary reading (different insights, more quantities of theoretical problem sets, etc.) and then proceed to the applied/computational LA texts and the advanced LA texts (Roman). Will I be in a disadvantageous position by skipping Axler and Treil?