Normal to what
OPs basic
Wtf is an eigenspace. I just learned about eigen vectors 💀
I mean I can guess I suppose
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.
Neat actually, and it fits into my understanding of linear algebra pretty well
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™️
did you learn about eigenvectors? or did you just memorize what you needed to pass linear algebra?
I learned enough about eigenvectors to handle differential equations lmao. Never took linear algebra
I did watch the 3blue1brown series on linear algrebra tho
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!"
After having looked them up they don't seem that bad. Am I missing something?
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.
[ X ] Doubt
I will only ever give you nilpotent matrices
degenerate ❤️ singular 💜 defective 🖤
