Alternative to Axler's "Linear Algebra Done Right"

I have been using Axler's "Linear Algebra Done Right." In fact I have recommended it here often.

I was wondering if there is a text at that level or higher that uses "kernel" rather than "null space"? And that does not go so far out of it's way to avoid matrices.

Thanks.

If Linear Algebra Done Right doesn't work, then try Linear Algebra Done Wrong, by Sergei Treil. This seems to meet both of your requirements.

If you want a higher level textbook, allow me to suggest "Advanced Linear Algebra" by Steven Roman.

The text is primarily concerned with abstract vector spaces, but it does treat matrices in detail and uses them when it is natural to do so. It will probably also cover all the linear algebra you need in an undergraduate degree. You can read samples of it here:

http://books.google.com/books?id=FV_s8W58D4UC&hl

http://www.amazon.com/Advanced-Linear-Algebra-Graduate-Mathematics/dp/0387728287

I'm a fan of the book by Hoffman and Kunze. It's a standard, concise, proof-based text.

There is A Terse Introduction of Linear Algebra, which rapidly overview the subject matter of a typical first course in an elegant way. Particularly, it does prefer the kernels over the null space. A free and legal draft of this book is available at here.

1. [GSM], Dym, Linear Algebra in Action
2. [GTM], Roman, Advanced Linear Algebra
3. Lax, Linear Algebra and its Applications
4. [UTM], Halmos, Finite-Dimensional Vector Spaces
5. [UTX], Curtis, Abstract Linear Algebra

These are both highly reputed and depth with high quality.

For simple computations and basic concepts, it could be obtained by any textbook or even lecture notes adequately.

For theory, it could be much more benefited to carefully select highly deep books.