The approach is developmental.
Although it covers the requisite material by proving things, it does not assume that students are already able at abstract work.
Instead, it proceeds with a great deal of motivation, many computational examples, and exercises that range from routine verifications to (a few) challenges.
The goal is, in the context of developing the usual material of an undergraduate linear algebra course, to help raise each student's level of mathematical maturity.
Orthogonal Publishing L3c Linear algebra, paperback/jim hefferon
