Second Textbook in Linear Algebra after Strang

[Noxide]

I used Gilbert Strang's text: Introduction to Linear Algebra, to introduce myself to the subject. The book drops off after giving a brief introduction to Linear Transformations. Can someone recommend a second text in Linear algebra that begins with Linear Transformations and develops the subject from there? I would prefer a more rigorous treatment, but the subject itself fascinates me and I would just like to continue onward from where I left off.

 

[Fredrik]

I like Axler. You can find other recommendations in the science book forum under academic guidance.

 

[nicksauce]

Axler!

 

[PieceOfPi]

I third Axler too. His book is short, so some people might think he omitted some other important concepts that should be covered in a second linear algebra course, but I think the book does a really good job tackling linear algebra with rigor. His writing style was great, proofs were pretty clear, and there were plenty of challenging (but good) problems in the book as well.

 

[Newtime]

While I definitely second all the Axler recommendations, I would also like to add Roman's "Advanced Linear Algebra." It's a grad textbook, so it's very dense and encyclopedic, but the first and second chapter (and third if you're interested) cover what you want in exceptional rigor.

 

[Pinu7]

Luckily for you, there are lots of great books on linear algebra.

Linear Algebra Done Right by Shelden Axler

And perhaps complement that by

Linear Algebra- Shilov (a Dover) (Note: This was the first Linear algebra book that I learned from)

I like both books a lot.

A book from a algebraic perspective which I also adore is

Advanced Linear Algebra- Roman

 

[Landau]

Also, Linear Algebra by Peter Lax is great (but expensive).

 

[abelgalois]

Linear Algebra Done Wrong, by Sergei Treil might just be what you're looking for:

Another detail is that I introduce linear transformations before teach-
ing how to solve linear systems. A disadvantage is that we did not prove
until Chapter 2 that only a square matrix can be invertible as well as some
other important facts. However, having already dened linear transforma-
tion allows more systematic presentation of row reduction. Also, I spend a
lot of time (two sections) motivating matrix multiplication. I hope that I
explained well why such a strange looking rule of multiplication is, in fact,
a very natural one, and we really do not have any choice here.

Not only does it look great but it's FREE:

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