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Eigenvector math problem

  1. May 25, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose that v is an eigenvector of both A and B with corresponding eigenvalues lambda and mui respectively. Show that v is an eigenvector of A+B and of AB and determine the corresponding eigenvalues


    2. Relevant equations



    3. The attempt at a solution
    Av = lambda*v
    Bv = mui*v
    this is all i can think of....can someone give me a hint abt the next step?
     
  2. jcsd
  3. May 25, 2009 #2

    Pengwuino

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    Gold Member

    Re: Eigenvalues

    Add the two equations together, tada! Of course, you'll need to exploit associativity... or linearity... man im always getting terms confused.
     
    Last edited: May 25, 2009
  4. May 25, 2009 #3
    Re: Eigenvalues

    u mean like:
    (Av +Bv) = lambda*v + mui*v
    (A+B)v = (lambda + mui) v
     
  5. May 25, 2009 #4

    Pengwuino

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    Gold Member

    Re: Eigenvalues

    Yup! As for finding the eigenvalues of AB, simply multiply AB by v and remember that your eigenvalues are scalars that can move freely.
     
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