God knows how I passed 4 years of engineering math without ever being able to describe to anyone what eigen* actually are, but I think that's actually the norm.
That's completely normal and very unfortunate. I only learned about the geometry of the eigen*s from an EE professor who loved math.
Unfortunately, the history of the eigen*s is rooted in the opaque and cryptic (but rigorous) linear algebra definition, and the non-rigorous but meaningful geometry came later.
