Which linear algebra textbook?

[scimaths]

Hi, I've searched this forum and narrowed my choices down to these three books:

linear algebra - friedberg
linear algebra - hoffman &kunze
linear algebra - serge langCould anyone please compare these three books?

I'm a high school student and haven't studied linear algebra before. (I can find determinants of 3x3 matrix, find eigenvalues and eigenvectors, etc but I guess this doesn't really count as linear algebra!)

I've already got Basic Linear Algebra by Blyth and Robertson and hoping to work through this book. Which of those three books will complement Blyth&Robertson's book?

I'm leaning towards Serge Lang. I prefer something that's concise and easy to follow. What do you think? Any help would be appreciated. :)edit; Also, how is Linear Algebra: An Introductory Approach bur Curtis? or Linear Algebra done right by Axler?

 

[micromass]

All three of the books are pretty good. But the books are also fairly rigorous. You should have some experience with matrices before trying out those books (but you said you have such experience, so that's good).

You really can't go wrong with any of Lang's books, he's an insanely famous mathematician and an awesome writer. If "Linear Algebra" is too difficult, then Lang also has an easier "Introduction to Linear Algebra" book.

Hoffman and Kunze is really not meant as a first course. It's an extremely good book, but don't use this one yet.

Friedberg is very nice, but I prefer Lang's books.

How much experience do you have with proofs by the way??

 

[scimaths]

All three of the books are pretty good. But the books are also fairly rigorous. You should have some experience with matrices before trying out those books (but you said you have such experience, so that's good).

You really can't go wrong with any of Lang's books, he's an insanely famous mathematician and an awesome writer. If "Linear Algebra" is too difficult, then Lang also has an easier "Introduction to Linear Algebra" book.

Hoffman and Kunze is really not meant as a first course. It's an extremely good book, but don't use this one yet.

Friedberg is very nice, but I prefer Lang's books.

How much experience do you have with proofs by the way??

Not much; stuff I've learned through books: proof by contradiction, induction, pigeon hole principles and such.

Thanks for your advice.

 

[verty]

I have Axler, it is pretty nice in that it has very few words, so chapters are short but dense in content. Half the book is about vector spaces and half is about linear operators, but the operator half is pretty dry with no pictures or examples, it is almost a second book for that purpose too. (How can one appreciate what normal operators are without examples?)

 

[scimaths]

All three of the books are pretty good. But the books are also fairly rigorous. You should have some experience with matrices before trying out those books (but you said you have such experience, so that's good).

You really can't go wrong with any of Lang's books, he's an insanely famous mathematician and an awesome writer. If "Linear Algebra" is too difficult, then Lang also has an easier "Introduction to Linear Algebra" book.

Hoffman and Kunze is really not meant as a first course. It's an extremely good book, but don't use this one yet.

Friedberg is very nice, but I prefer Lang's books.

How much experience do you have with proofs by the way??

I have Axler, it is pretty nice in that it has very few words, so chapters are short but dense in content. Half the book is about vector spaces and half is about linear operators, but the operator half is pretty dry with no pictures or examples, it is almost a second book for that purpose too. (How can one appreciate what normal operators are without examples?)

Thanks. Do you know anything about this book?:
http://www.amazon.com/Linear-Algebra-Oxford-Science-Publications/dp/0198502370/ref=sr_1_1?ie=UTF8&qid=1370094368&sr=8-1&keywords=kaye+wilson+linear+algebra

I just looked up syllabus for uni I'm going to in September and this was in the recommended book list for 1 year and 2nd year.

I'm hoping to get this and get one other book that will supplement this well.

It would be great if one of Lang, Axler, Friedberg's books are a bit different from LA by Kaye and Wilson. Which one would be the best in this case?

 

[mathwonk]

all three of those books are good, but they are very different. Friedberg (and Insel and Spence) is the most elementary and detailed, with a lot of examples of concrete calculations. Thi book is suitable for the average student. Lang is more sparse, it explains the basic theory very clearly but has far fewer examples and details. Like most of Lang's books, it is not sufficient to master the subject, and appeals to students who can benefit from a brief theoretical explanation.. I might suggest combining Lang with Friedberg. Hoffman and Kunze is a very detailed but fairly abstract treatment of the subject and as micromass said, is most suitable after reading the others. So i would suggest reading first either Lang or Friedberg and then the other, or both together, and afterwards, Hoffman and Kunze. If you can only read one it should probably be Friedberg, but if you read all three, you will know the subject very well. Axler, like Lang, is a too brief and theoretical discussion to be your only source, but it is excellent as a second or third reading. Friedberg is the only truly beginning book on your list.

 

[Sankaku]

Mathwonk's advice is excellent. Unfortunately some students even find Friedberg too abstract (However, I think it is excellent). There are a number of good free e-textbooks available if you want to wait on buying a book. Each has its own style, so look around a bit.

http://joshua.smcvt.edu/linearalgebra/

http://www.math.brown.edu/~treil/papers/LADW/LADW.html

http://linear.ups.edu/

Libraries are also good, if you have access to one with textbooks.

 

[Sankaku]

Thanks. Do you know anything about this book?:
http://www.amazon.com/Linear-Algebra-Oxford-Science-Publications/dp/0198502370/ref=sr_1_1?ie=UTF8&qid=1370094368&sr=8-1&keywords=kaye+wilson+linear+algebra

I just looked up syllabus for uni I'm going to in September and this was in the recommended book list for 1 year and 2nd year.

What country are you in? That book looks like it is aimed at 2nd year students in the UK and is probably fairly abstract. From looking at the table of contents, it might be comparable to (or slightly beyond) the level of Axler (but probably different in style).

 

[mathwonk]

a good truly beginning book is elementary linear algebra, by paul shields.

 

[verty]

Here is a nice looking book that may help bridge the gap between the elementary books and the abstract:

Linear Algebra & Matrix Theory by Robert R. Stoll

It may all depend on the reader which book is suitable.

 

[verty]

Thanks. Do you know anything about this book?:
http://www.amazon.com/Linear-Algebra-Oxford-Science-Publications/dp/0198502370/ref=sr_1_1?ie=UTF8&qid=1370094368&sr=8-1&keywords=kaye+wilson+linear+algebra

My thoughts are exactly in line with what Sankaku said. A comprehensive looking book but perhaps difficult to learn from.

 

[mathwonk]

heres a freebie some people like:

http://joshua.smcvt.edu/linearalgebra/