31–40 of 48 posts
That was an excellent explanation of the intuition and motivation behind eigenvectors. Eigenvectors are also used extensively in pattern recognition. Notably, in facial recognition: http://en.wikipedia.org/wiki/Eigenface
Earlier quoted context omitted.
Ok, others have tried a little bit of the math, but this is a difficult form for that. So here is a very intuitive (i.e. hand-wavy) way to think about the type of relationships we are talking about. Suppose you have a (finite) cloud of points in three dimensions. For example, a bunch of GPS measurements. Lets just imagine that they are roughly elliptical, stretched out like a football. For simplicity we'll subtract t…
So there's one part of the explanation on the page that I don't quite get: she uses the example of a coin being turned 360 degrees along some axis as leaving all possible vectors as eigenvectors: "If you rotate a coin by 360 degrees you preserve all directions and so each direction is an eigenvector. Because no stretching has occurred, all of these eigenvectors have eigenvalue 1. Rotating the coin by 60 degrees destr…
"Prove that A and A-Inverse have the same Eigen Values and corresponding Eigen Vectors."
The solution to this made no sense, but I managed to memorize it so that I could pass the test.
Forest through the trees?
It depresses me a bit that in college I knew exactly what all this was... for a month... until the day after I was tested on it.
Earlier quoted context omitted.
> 1. A linear mapping is not a "kind of equivalence" by any reasonable definition. For instance, the function that maps every vector to 0 is a linear mapping, and it has plenty of eigenvectors. (All with eigenvalue 0.) Linear mappings are the homomorphisms between vector spaces. So they are a "kind of equivalence". See for example http://en.wikibooks.org/wiki/Linear_Algebra/Definition_of_Ho...
The zero mapping is a homomorphism. I would not call it a "kind of equivalence"; would you?
It depresses me a bit that in college I knew exactly what all this was... for a month... until the day after I was tested on it.
This would have been very helpful to have a grasp of for my research in university where I had to explain eigenvalues and eigenvectors to fellow computer science people. It probably also would have helped me understand what the hell my own code did.
Earlier quoted context omitted.
Look, I am good at Math. I even love Number Theory. But what you wrote scares me. Can I run away now? (I hope to one day be able to look at it and say 'my, that is so simple...' like I do with high school math)
This is the problem I had with Linear Algebra. The first half of the class felt like I was just being drilled definitions. But once all the definitions click, it's rather simple.