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Homework Help: Eigenvalues and eigenvectors of a linear transform

  1. Apr 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Find all the eigenvalues and eigenvectors of the linear transformation:
    T(f) = 5f ' -3f
    T: from C^(nfnty) --> C^(nfnty)
    where C^(nfnty) is set of continuously functions

    2. Relevant equations

    A scalar B is called an eigenvalue of T if there exists a nonzero element f of C such that:
    T(f) = Bf

    3. The attempt at a solution

    didn't know where to start
  2. jcsd
  3. Apr 24, 2007 #2

    matt grime

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    You do know where to start. You have said you need to find all functions f and a scalars, B so that


    so find them. That part is first year calculus: first order linear homogeneous differential equation.
  4. Apr 24, 2007 #3


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    T(f)=Bf so 5*f'-3*f=B*f. It's an ODE. Solve it.
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