I read Geometric Approach, which should be completely straightforward for anyone at the level of Axler's LA book. It's very applied, a pretty easy read. I have the impression that Geometric Primer aimed at an even broader audience, students well outside of math/stats.
Also along these lines, The Geometry of Multivariate Statistics, Thomas D. Wickens
The Geometry of Multivariate Statistics is by far the best in my view, as it presents the geometric/visual intuition.