1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

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

    5f'-3f=Bf


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

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    T(f)=Bf so 5*f'-3*f=B*f. It's an ODE. Solve it.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?