It’s not about not teaching the platonic definition.
The problem is that you don’t start at the platonic definition. Mathematicians don’t start there either, they start at a problem. The problem may even be a hole in some other platonic idea, but nothing is ever self-contained Platonism… except maybe for categories, but well, the problem it looks is how far pure Platonism can get you.
Yes, people teach mathematics wrong. It should start from application, and only then get formalized.
A large part of the problem is that we put people that study pure math deciding how to teach it.
The problem is that the eigenvector is the thing that satisfies the equation he showed you. That’s what it is.
Mathematics is full of completely unsatisfying answers, and only when apply it you get any meaningful idea why those things exist. But those are not their definition.
That one is “evidently”. It wasn’t obvious until you tried.
Well, that’s not reason not to try.
No, you are at the top. If you were at the center you wouldn’t need a level to tell you.