this post was submitted on 21 Oct 2025
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I had a linear algebra professor who did that all the time. Never did figure out what an eigenvector is not why I would want 14 ways of finding one. Brilliant man, terrible teacher.
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.
The problem I had is that taking one assortment of numbers that had no meaning, doing a bunch of operations on them (never actually finishing the operations though, because the last steps were "obvious") leading to a different arrangement of numbers that also meant nothing, was not a good method of teaching. The pass/fail rate of that course relative to all the others reflected that. Every other teacher/professor I had before or since would include context when introducing an entirely new concept.
I had the opposite problem when I was learning linear algebra. The professor kept things at the most abstract and generic level, which made it hard to understand what was going on, because it felt like everything was “the thing is defined as the thing”. I don’t think it fully clicked for me until I took another class that involved some actual numerical applications of those ideas.