Robert J. Valenza 
Linear Algebra [PDF ebook] 
An Introduction to Abstract Mathematics

Based on lectures given at Claremont Mc Kenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational – for example by connecting matrices to linear transformations from the outset – and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.