4 ms·

Eigenvectors and Eigenvalues show up everywhere, although sometimes it's in the form of an iterative estimate (PageRank is basically the power method estimation

Eigenvectors and Eigenvalues show up everywhere, although sometimes it's in the form of an iterative estimate (PageRank is basically the power method estimation of the first eigenvector of a connected graph of web pages). They're in the same class as logarithms and Fourier transforms IMHO. You won't need to calculate them by hand, but you should know what they do and why they're important.

xevb3k 8y ago
Interesting, perhaps that’s it... I’ve used FFTs a few times, but even FFTs have never been make or break in terms of getting a pipeline or analysis working well.
- cowboysauce 8y ago
  The Fourier transform is actually linked with linear algebra. You can think of it as taking a vector in an infinite dimensional Hilbert space (your signal) and decomposing it into its components (the amplitudes of the frequencies).
  - stephencanon 8y ago
    The Fourier transform as used in practice in signal processing is ~always discrete, hence finite-dimensional. It's literally "just" a rotation with an especially nice decomposition that allows efficient multiplication.
    - danharaj 8y ago
      A particular fft in practice may be discrete but the relation between fft's of different resolutions of the "same" signal hints at the infinite structure which bundles up all the finite subspaces into one conceptual object.
WhompingWindows 8y ago
Why should you know what they do and why they're important? How does that practically change my R code?
- angersock 8y ago
  Because, say, knowing about Fourier transforms can help you write more efficient filtering or open up new ways to view your data--perhaps there's a really interesting behavior in the frequency domain you'd miss otherwise. If you just want to be a statistical script kiddie you do you. :)
  - ItsMe000001 8y ago
    When working with real world data almost everything is more important than being able to use the most abstract methods "to extract the last bit of data". It's often extremely fuzzy to begin with, the collection process to what it represents, for me, while I love math and see it as the "magical language" in a magical world, I find common sense and a certain kind of work ethics go soooo much further than any math Ph.D. I (with a CS degree) wanted to start another study (over a decade later, thirsting for new theory and new knowledge) and chose math - but that was around the same time edX and Coursera etc. got up and running with loads of courses, and I ended up ditching the additional math degree for loads and loads of courses in fields like medicine and biology, deciding to go for breadth instead. Of course, that's purely personal and even as an anecdote not worth much to anyone. It's just that I too got disillusioned with (higher and higher) math as an helpful tool in practical life. Of course I still see the benefits in many fields, but I think a surprisingly low number of very good specialists may be all we need. The rest of us can just ask them when we actually do need something. Right now I'm taking a "math. modeling" course. Still, the only use case I ever found was... other courses! I already modeled a little bit in a biology course. Sure, in real life I could model this or that, but the truth is that a very rough estimate guided by experience and "feeling" has always been enough. There are too many variables that cannot be accurately measured, so going for a nice model is kind of useless. For example, I was just asked today about the performance of the crypto-hash-connected data storage and exchange library I wrote. Now that sounds like something I could model! Only experience tells me that's useless. The only worthwhile answer is to set up a concrete scenario, with a concrete app using it, concrete network and concrete systems, and test it. Could be anything from smartphones to well-connected servers. Sure I could create a sophisticated model and simulation - and it would be useless. Maybe I'm just a bit, or more than just a bit, disappointed that all the considerable amount of math I learned in my life didn't seem to be of nearly as much use as I would have hoped. I'm also frustrated each time such a topic comes up and everyone is so excited about how great it is, and I always feel like I'm missing something despite trying hard, like the color blind guy looking at paintings. I mean the usefulness to me, not understanding it.
madengr 8y ago
I use logarithms and FFTs daily, but got a C in Linear Algebra, after getting A in all other EE/Math/Phys courses. It kicked my ass once we got to proofs.

xevb3k 8y ago

Interesting, perhaps that’s it... I’ve used FFTs a few times, but even FFTs have never been make or break in terms of getting a pipeline or analysis working well.

cowboysauce 8y ago
The Fourier transform is actually linked with linear algebra. You can think of it as taking a vector in an infinite dimensional Hilbert space (your signal) and decomposing it into its components (the amplitudes of the frequencies).
- stephencanon 8y ago
  The Fourier transform as used in practice in signal processing is ~always discrete, hence finite-dimensional. It's literally "just" a rotation with an especially nice decomposition that allows efficient multiplication.
  - danharaj 8y ago
    A particular fft in practice may be discrete but the relation between fft's of different resolutions of the "same" signal hints at the infinite structure which bundles up all the finite subspaces into one conceptual object.

WhompingWindows 8y ago

Why should you know what they do and why they're important? How does that practically change my R code?

angersock 8y ago
Because, say, knowing about Fourier transforms can help you write more efficient filtering or open up new ways to view your data--perhaps there's a really interesting behavior in the frequency domain you'd miss otherwise. If you just want to be a statistical script kiddie you do you. :)
- ItsMe000001 8y ago
  When working with real world data almost everything is more important than being able to use the most abstract methods "to extract the last bit of data". It's often extremely fuzzy to begin with, the collection process to what it represents, for me, while I love math and see it as the "magical language" in a magical world, I find common sense and a certain kind of work ethics go soooo much further than any math Ph.D. I (with a CS degree) wanted to start another study (over a decade later, thirsting for new theory and new knowledge) and chose math - but that was around the same time edX and Coursera etc. got up and running with loads of courses, and I ended up ditching the additional math degree for loads and loads of courses in fields like medicine and biology, deciding to go for breadth instead. Of course, that's purely personal and even as an anecdote not worth much to anyone. It's just that I too got disillusioned with (higher and higher) math as an helpful tool in practical life. Of course I still see the benefits in many fields, but I think a surprisingly low number of very good specialists may be all we need. The rest of us can just ask them when we actually do need something. Right now I'm taking a "math. modeling" course. Still, the only use case I ever found was... other courses! I already modeled a little bit in a biology course. Sure, in real life I could model this or that, but the truth is that a very rough estimate guided by experience and "feeling" has always been enough. There are too many variables that cannot be accurately measured, so going for a nice model is kind of useless. For example, I was just asked today about the performance of the crypto-hash-connected data storage and exchange library I wrote. Now that sounds like something I could model! Only experience tells me that's useless. The only worthwhile answer is to set up a concrete scenario, with a concrete app using it, concrete network and concrete systems, and test it. Could be anything from smartphones to well-connected servers. Sure I could create a sophisticated model and simulation - and it would be useless. Maybe I'm just a bit, or more than just a bit, disappointed that all the considerable amount of math I learned in my life didn't seem to be of nearly as much use as I would have hoped. I'm also frustrated each time such a topic comes up and everyone is so excited about how great it is, and I always feel like I'm missing something despite trying hard, like the color blind guy looking at paintings. I mean the usefulness to me, not understanding it.

madengr 8y ago

I use logarithms and FFTs daily, but got a C in Linear Algebra, after getting A in all other EE/Math/Phys courses. It kicked my ass once we got to proofs.