(1) Axler's "Linear Algebra Done Right"

...a nice introduction to abstract linear algebra, but not quite abstract or terse enough.

(2) These course notes: http://www.math.mcgill.ca/goren/AlgebraII07-08/AlgebraII.htm

...good, though the duality section is a bit lacking. Riesz Representation Theorem FTW!

While it certainly isn't terse, Linear Algebra by Friedberg, Insel, and Spence is comprehensive and rigorous. It has everything you would ever want to know about linear algebra with some applications too.