Comment on I'm too stupid for this
IrateAnteater@sh.itjust.works 5 months agoI 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.
When you multiply a matrix and a vector, you get a new vector. An eigenvector of a matrix means the output and input vectors are pointing in the same direction.
These are important for various real-world applications, but more explanation would probably have to be context specific.
So… Like to find the optimal impact angle to send an object towards a target?
The largest eigenvector would be the most probable direction of the struck object after impact?
Usually it is something like the eigenvectors represent stable states of the system, and other states will tend to be unstable until and end up in one of those stable states.
For example, the eigenvectors of the moment of inertia tensor represent “principle axes” of rotation, and these represent the possible stable axes of rotation (usually only one or two axes is actually stable, it depends on the object).
By analyzing principle axes of inertia, you can explain why a frisbee’s rotation is very stable around one axis but unstable around all other axes. And you can predict this kind of behavior for other objects.
Another example is in quantum mechanics, eigenvectors correspond to states that result after “measurement collapse” of the wavefunction, and are useful in various quantum mechanics problems, such as predicting the behavior of atoms, molecules, or semiconductors.
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.
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.
As someone both studying and teaching math: there should be two different ways to teach math - for other mathematicians and for non-mathematicians.
For mathematicians you want to use all the formal proofs and sharp definitions and so on. But we have so much fun teaching that way, we forget when we switch classes that engineers don’t like/care/are motivated to think the same way. We should pivot towards application-based, result-oriented teaching but we often just don’t. And students have to deal with it because the other class managed (pure mathematicians).
An eigenvector is just kind of the direction the matrix is pointing
Is this why Neo became One?
Well duh, obviously.
prole@lemmy.blahaj.zone 5 months ago
This sounds exactly like my experience with that subject in college. Makes me wonder if it’s the same guy, or if they’re just all like that. Don’t think I can remember his name anyway.