184

eigenspaces (mander.xyz)

submitted 7 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz

18 comments fedilink hide all child comments

top 18 comments

sorted by: hot top controversial new old

[-] match@pawb.social 15 points 7 months ago

Normal to what

[-] Batman@lemmy.world 3 points 7 months ago

OPs basic

[-] sharkfucker420@lemmy.ml 12 points 7 months ago

Wtf is an eigenspace. I just learned about eigen vectors 💀

I mean I can guess I suppose

[-] jxk@sh.itjust.works 22 points 7 months ago

You want an answer?

So you've probably learned that if u is an eigenvector, then multiplying u by any scalar gives you another eigenvector with the same eigenvalue. That means that the set of all a*u where a is any scalar forms a 1-dimensional space (a line if this is a real vector space). This is an eigenspace of dimension one. The full definition of an eigenspace is as the set of all eigenvectors of a given eigenvalue. Now, if an eigenvalue has multiple independent eigenvectors, then the set of all eigenvectors for that eigenvalue is is still a linear space, but of dimension more than one. So for a real vector space, if an eigenvalue has two sets of independent eigenvectors, its eigenspace will be a 2-dimensional plane.

That's pretty much it.

[-] sharkfucker420@lemmy.ml 5 points 7 months ago

Neat actually, and it fits into my understanding of linear algebra pretty well

[-] skulblaka@startrek.website 9 points 7 months ago

I, a mere mortal, have no idea what the fuck this meme is talking about and I am slightly afraid. This sounds like Deep Math™️

[-] match@pawb.social 1 points 7 months ago

did you learn about eigenvectors? or did you just memorize what you needed to pass linear algebra?

[-] Ziglin@lemmy.world 4 points 7 months ago

I "learned" about them for quantum computing (I think that's mostly linear algebra). I was kind of disappointed they're just vectors I somehow expected them to do something weird (based off the name).

[-] myslsl@lemmy.world 3 points 7 months ago

My experience with eigenstuff has been kind of a slow burn. At first it feels like "that's it?", then you do a bunch of tedious calculations that just kind of suck to do... But as you keep going they keep popping up in ways that lead to some really nice results in my opinion.

[-] Ziglin@lemmy.world 2 points 7 months ago

I guess it's the same for me but I just kind of think of it as vector stuff not eigen* stuff.

[-] sharkfucker420@lemmy.ml 2 points 7 months ago* (last edited 7 months ago)

I learned enough about eigenvectors to handle differential equations lmao. Never took linear algebra

I did watch the 3blue1brown series on linear algrebra tho

[-] niktemadur@lemmy.world 8 points 7 months ago

Later back at the lab, after trusting this guy, all the boys with their white robes and clipboards scratching their heads: "The Eigenvalue is off the charts!"

[-] gregorum@lemm.ee 4 points 7 months ago

[ X ] Doubt

[-] Ziglin@lemmy.world 4 points 7 months ago

After having looked them up they don't seem that bad. Am I missing something?

[-] myslsl@lemmy.world 3 points 7 months ago* (last edited 7 months ago)

Eigenvectors, values, spaces etc are all pretty simple as basic definitions. They just turn out to be essential for the proofs of a lot of nice results in my opinion. Stuff like matrix diagonalization, gram schmidt orthogonalization, polar decomposition, singular value decomposition, pseudoinverses, the spectral theorem, jordan canonical form, rational canonical form, sylvesters law of inertia, a bunch of nice facts about orthogonal and normal operators, some nifty eigenvalue based formulas for the determinant and trace etc.