Is Axler's Determinant-Free Approach to Linear Algebra Worth Studying?

[SeReNiTy]

Hi guys, During the upcoming summer break I want to patch up my linear algebra skills while researching with my professor. I've already taken a course on linear algebra, but frankly it was rather elementary. This semester after taken courses on differential geometry and further analysis I've realized I'm lacking a lot of the linear algebra required...

So to patch in this gap (more like abyss) I've decided to study a proper course on linear algebra. So my question is what should i cover in my syllabus and what textbook should i use? Previously, I've studied the whole Anton book and I've heard good things about the Friedberg book.

 

[Rach3]

Try Axler - it's a cheap paperback with very clear exposition, and proofs that are obviously directed at the undergraduate (carefully thought through and pedagogic). It's a "second course in Linear algebra" according to the author, though it can act as a somewhat intensive first introduction. Unlike Anton, which according to Amazon is "an introduction for... engineering and computer science students", Axler is very much applications-free pure math, there are no matrix-factorization algorithms or problems relating to moments of inertia (things very useful outside of pure math). A less friendly but much more expansive book, at a similar or slightly higher level than Axler, is Hoffman & Kunze.

I take it you're going into mathematics by the courses you've mentioned (analysis, differential geometry). Axler is desgined for students in that position - there are many more 'practical' linear algebra books targeting engineers, and economics majors - they're very different in scope.

 

[SeReNiTy]

I'm heading into the field of theoretical physics, but the theory i want to study requires a extensive knowledge of mathematics, what do you think about the friedbeg book? I heard it is the best.

 

[Rach3]

Then I recommend Axler even more highly. It's good at teaching intution, so it's excellent preparation for quantum mechanics especially, and differential geometry (which you seem to have already studied...) besides uncountable other benefits.

I don't know Friedberg, but I doubt it could be as pedagogic as Axler with his marvelous, determinant-free proofs.

 

[leon1127]

Look at Matrix Analysis and Topics in Matrix Analysis by Horn and Johnson.

 

[SeReNiTy]

I don't know Friedberg, but I doubt it could be as pedagogic as Axler with his marvelous, determinant-free proofs.

Give me a example of one of his determinant-free proofs? I quite liked proofs with wedge products and determinants in diff geom...But i must admit getting your head around the determinant can be tricky!

 

[devious_]

Axler and Friedberg are both excellent texts. Friedberg covers MUCH more material, though. On the other hand you might find Axler's determinant-free approach to be more to your liking.

 

[SeReNiTy]

Axler and Friedberg are both excellent texts. Friedberg covers MUCH more material, though. On the other hand you might find Axler's determinant-free approach to be more to your liking.

Can someone provide me with a example of his determinant free proofs...