1. Limited time only! Sign up for a free 30min personal 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!

Math induction

  1. Apr 17, 2010 #1
    Let [tex]\lambda[/tex] be an eigenvalue of [tex]A[/tex] and let [tex]\mathbf{x}[/tex] be an eigenvector belonging to [tex]\lambda[/tex]. Use math induction to show that, for [tex]m\geq1[/tex], [tex](\lambda)^m[/tex] is an eigenvalue of [tex]A^m[/tex] and [tex]\mathbf{x}[/tex] is an eigenvector of [tex]A^m[/tex] belonging to [tex](\lambda)^m[/tex].


    [tex]p(1): A^1\mathbf{x}=(\lambda)^1\mathbf{x}[/tex]\

    [tex]p(k): A^k\mathbf{x}=(\lambda)^k\mathbf{x}[/tex]

    [tex]p(k+1): A^{k+1}\mathbf{x}=(\lambda)^{k+1}\mathbf{x}[/tex]

    Assume p(k) is true.

    Since p(k) is true, [tex]p(k+1): A*(A^k\mathbf{x})[/tex]

    Not sure if this is correct path to take to the end result. Let alone, if it is if I am going about it right.
    Last edited: Apr 17, 2010
  2. jcsd
  3. Apr 17, 2010 #2


    User Avatar
    Science Advisor
    Homework Helper

    You were doing ok, except you don't want A^(k+1)(lambda). You want p(k+1): A^(k+1)(x)=A*(A^k(x))=A*(lambda^k*x)=lambda^k*A(x)=???
  4. Apr 17, 2010 #3
    Ok I gotcha.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Math induction
  1. Induction math problem (Replies: 2)

  2. Math induction (Replies: 30)