eigenspaces

Comments

• match@pawb.social ⁨6⁩ ⁨months⁩ ago

  Normal to what

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  • Batman@lemmy.world ⁨6⁩ ⁨months⁩ ago

    OPs basic

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• sharkfucker420@lemmy.ml ⁨6⁩ ⁨months⁩ ago

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

  I mean I can guess I suppose

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  • jxk@sh.itjust.works ⁨6⁩ ⁨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 ⁨6⁩ ⁨months⁩ ago

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

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  • skulblaka@startrek.website ⁨6⁩ ⁨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 ⁨6⁩ ⁨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 ⁨6⁩ ⁨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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    • sharkfucker420@lemmy.ml ⁨6⁩ ⁨months⁩ ago

      I learned enough about eigenvectors to handle differential equations lmao

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• niktemadur@lemmy.world ⁨6⁩ ⁨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!”

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• Ziglin@lemmy.world ⁨6⁩ ⁨months⁩ ago

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

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  • myslsl@lemmy.world ⁨6⁩ ⁨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.

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• yetAnotherUser@feddit.de ⁨6⁩ ⁨months⁩ ago

  I will only ever give you nilpotent matrices

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  • match@pawb.social ⁨6⁩ ⁨months⁩ ago

    degenerate ❤️ singular 💜 defective 🖤

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• gregorum@lemm.ee ⁨6⁩ ⁨months⁩ ago

  [ X ] Doubt

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• Zerush@lemmy.ml ⁨6⁩ ⁨months⁩ ago

  tube.kuylar.dev/watch?v=U6Rzp1FQPao

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