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Prove null is invariant

  1. Feb 21, 2008 #1
    Suppose S, T [tex]\in[/tex] L(V) are such that ST=TS. Prove that null(T-[tex]\lambda[/tex]I) is invariant under S for every [tex]\lambda[/tex] [tex]\in[/tex] F.


    I can't find anything helpful in my book, I'm not sure where to start...
     
  2. jcsd
  3. Feb 21, 2008 #2

    Dick

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    null(T-lambda*I) is just the set of all vectors x such that (T-lambda*I)x=0. So Tx-lambda*x=0. Or Tx=lambda*x. To show this is invariant under S you just have to show that if x satisfies that property, then so does Sx.
     
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