Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Eigenvalue as a generalization of frequency

  1. Aug 1, 2016 #1
    Hello everyone.
    I understand the concept of eigenvalues and eigenvectors, using usually a geometric intuition, that a eigenvectors of a matrix M are stretched by the corresponding eigenvalue, when transformed through M.

    My professor said that eigenvalues represent a generalization of the concept of frequency.
    I can not recall the context though.
    Can someone provide an short explanation and/or some (not too technical) reading material?

    Thanks.
     
  2. jcsd
  3. Aug 1, 2016 #2

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    Are you allowing complex eigenvalues and eigenvectors? They are rotations & expansions in a plane, which is related to frequency responses. If so, check out .
     
  4. Aug 1, 2016 #3
    Thanks.
    Did so, I dont understand how it's related to frequency though.
    Rotations per time would.
     
  5. Aug 1, 2016 #4

    FactChecker

    User Avatar
    Science Advisor
    Gold Member

    Rotations per unit time is the right idea. There are so many different contexts that matrix eigenstructures can be used in that it is hard to do more than give a general intuition. If the (complex) eigenvalue multiplication represents rotation in a unit time, then the amount of rotation in that time (the argument of the eigenvalue) does correspond to a frequency. And the magnitude of the eigenvalue corresponds to a gain (per unit time) at that frequency.

    PS. I hate to put words in your professor's mouth. You should probably ask him a follow-up question about what he meant.
     
  6. Aug 9, 2016 #5

    chiro

    User Avatar
    Science Advisor

    Hey npit,

    You might want to consider the spectral decompositon of PDP_inverse in terms of rotations and scalings.

    If you have an orthogonal matrix with R*R^t = I [meaning R^t = R_inverse] then you can make sense of a rotation occuring along with a scaling of each axes and then rotating back again.

    Co-ordinate system transformations have the same property (like in physical visualization and simulations) and it can help when the P matrices have the PP^t = I property.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Eigenvalue as a generalization of frequency
Loading...