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Eigenvalues,charateristic polynomial

  1. Oct 31, 2011 #1
    1. The problem statement, all variables and given/known data
    http://img213.imageshack.us/img213/7867/problemeigen.png [Broken]

    Uploaded with ImageShack.us

    2. Relevant equations
    http://img339.imageshack.us/img339/771/equationh.jpg [Broken]

    Uploaded with ImageShack.us


    3. The attempt at a solution

    so i tried doing the problem i gonna use L for lambda
    i got the matrix
    [1-L, 3]
    [K , 4-L]

    then i do determinant to get the characteristic polynomial
    (1-L)(4-L)-3K=0
    L^2-5L+4=3k
    K=(L^2-5L+4)/(3)

    the other way i did it but im not sure is [(L^2-5L+4)/(K)] -3

    i also tried doing this in matlab by doing
    k=-100:100
    a=[1 3; k 4;]
    but that i think would just put a bunch of numbers where k is i think
    not really sure how to proceed from here
     
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Oct 31, 2011 #2

    Deveno

    User Avatar
    Science Advisor

    i think what you are being asked to do is plot the function:

    k(L) = (1/3)(L2-5L+4)

    limiting the range (the "y" axis, or in this case, the "k" axis) to [-100,100]

    (so you can fit all L values that give output values within your range on the plot).
     
  4. Oct 31, 2011 #3

    Mark44

    Staff: Mentor

    Missing part of the lower right element.
    No, the idea is to solve for lambda (L here). k is just a constant.

    Solve this equation: λ2 - 5λ + 4 - 3k = 0. This is a quadratic in λ.
     
    Last edited by a moderator: May 5, 2017
  5. Oct 31, 2011 #4

    Deveno

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    Science Advisor

    that's what i get for not reading closely enough *facepalm*.

    right it should be L in terms of f(k).
     
  6. Oct 31, 2011 #5
    (λ-4)(λ-1)-3k
    λ=4
    λ=1

    i solved it but im not sure what im supposed to do with it though
     
  7. Oct 31, 2011 #6

    Mark44

    Staff: Mentor

    You're ignoring the -3k. And the above should be an equation; namely λ2 - 5λ + 4 - 3k = 0.

    Do you know how to solve quadratic equations?
     
  8. Oct 31, 2011 #7

    Mark44

    Staff: Mentor

    Happens to us all (well, it happens to me). Don't feel bad.
     
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