Comment on eigenspaces

sharkfucker420@lemmy.ml ⁨7⁩ ⁨months⁩ ago

• jxk@sh.itjust.works ⁨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.

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  • sharkfucker420@lemmy.ml ⁨7⁩ ⁨months⁩ ago

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

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• skulblaka@startrek.website ⁨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™️

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• match@pawb.social ⁨7⁩ ⁨months⁩ ago

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

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  • Ziglin@lemmy.world ⁨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).

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    • myslsl@lemmy.world ⁨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.

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      • Ziglin@lemmy.world ⁨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.

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  • sharkfucker420@lemmy.ml ⁨7⁩ ⁨months⁩ ago

    I learned enough about eigenvectors to handle differential equations lmao

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