[6gvONxR4sf7o]

> ... by clarifying the connections between these seemingly disparate systems.

This is the big reason I like it. I remember learning bits and pieces of linear algebra whose rules seemed so entirely random (vectors vs pseudo-vectors, curl, quaternions, some spin calculations I can't even remember anymore, etc), that turned out to have more unified geometric interpretations once I learned GA. It definitely slowed me down as a student who hated 'just memorize it' pedagogy.