ELI5- Eigenvalues and Eigenvectors?
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Scaling things up and down is very easy to work with and think about. It’s just zooming in and out. But if you can only zoom in and out, then you don’t have too much to work with. Luckily, we can zoom different directions in different ways. So I could vertically zoom in by a factor of 3 and horizontally zoom in by a factor of 10. This is kinda like a “mixed zoom”. (This would be the transformation (x,y)->(10x,3y).)
Eigen-stuff is just figuring out “mixed zooms”. To have a mixed zoom, you need the directions that you’re zooming in (the “eigenvectors”) and the factors by which you’re zooming (the “eigenvalues”). Important theorems in math tell us that *most* nice spacial transformations are actually “mixed zooms”, and eigenvector and eigenvalue methods are how to find these directions and scale factors. This, overall, simplifies work because we don’t have to deal with crazy, high dimensional transformations and can just think about different zooms in different directions.
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