Thank you - its too easy to get into the weeds with mathematics and lose the "why" of something. Connecting these higher level concepts with the algebra that _most_ people have experience with ends up being a more direct way to share knowledge vs diving into the higher level stuff that enthusiasts really enjoy.

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.