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Homework Help: Kernel "stable under": is my interpretation correct?

  1. Apr 16, 2008 #1
    [SOLVED] Kernel "stable under": is my interpretation correct?

    1. The problem statement, all variables and given/known data

    A1, A2, A3,..., Ar are endomorphisms. W is the kernel of Ar - lambda*I, where lambda is the eigenvalue of Ar. W is stable under A1, A2, A3,..., Ar-1. Question: does "stable under" equal "closed under", and is the following interpretation of this stability correct?

    For all elements u in W, Aku is an element in W.​
    Last edited: Apr 16, 2008
  2. jcsd
  3. Apr 16, 2008 #2


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    I believe so. I can't think what else it would mean.
  4. Apr 17, 2008 #3
    Ok, thanks!
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