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Smallest Eigenvalue

  1. Nov 16, 2012 #1
    Can someone help me with this question?

    I know we have to set up the auxiliary equation and then solve for λ but for some reason I am not getting the right answer.

    My equation is:

    m^2 + 4m + (5λ + 3) = 0

    then we get -2 ± sqrt(5λ-1)i

    Now can somebody explain what I have to do after this?
     

    Attached Files:

  2. jcsd
  3. Nov 16, 2012 #2

    Mark44

    Staff: Mentor

    You are assuming that 1 - 5λ < 0 or IOW, that λ > 1/5. Are you given any information about λ?

    I would break this into three cases:
    λ < 1/5, implying two real values of m.
    λ = 1/5, implying one real and repeated value of m; namely m = -2.
    λ > 1/5, implying two complex values of m.

    Since the question asks for the smallest eigenvalue, I take it that they are referring to the roots of the characteristic equation, or m. Also, since complex numbers aren't ordered (you can't compare them with < or >), I guess that limits things to the first two cases above.
     
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