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Math Help - Eigen space and dimension

  1. #1
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    Eigen space and dimension

    Linear transformation f:C(R) -> C(R)



    Eigen space and dimension-billede-2.png


    a) I have to set up the eigenvalue-problem and solve it :

    my solution : keλt

    b) Now I have to find the dimension of the single eigen spaces and plot the graph for 3 different vectors from each eigen space when λ is

    -5 and 0.

    I'm having some problems with this part. I I've chosen k as 2, 5 and 13 and then I just plot them with the two different λ values :

    k = 2

    2e-5t

    2e0t = 2


    k = 5

    5e-5t

    5e0t = 5


    k = 13

    13e-5t

    13e0t = 13


    Eigenspaces :

    E-5 = ke-5t

    E0=k

    But I don't know how to find the dimension of the single eigen spaces ?
    Attached Thumbnails Attached Thumbnails Eigen space and dimension-billede-1.png  
    Last edited by Tala; November 25th 2012 at 03:03 AM.
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