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Jordan canoncial form

  1. May 25, 2010 #1
    1. The problem statement, all variables and given/known data
    It is possible for a generalized eigenvector of a linear operator T to correspond to a scalar that is not an eigenvalue of T.


    2. Relevant equations
    There is a definition of generalized eigenvector of T corresponding to lamda.

    3. The attempt at a solution
    I know that this statement is false therefore I need a counter example, but I can't think of one since this statement contradict the definition of generalize eigenvector of T corresponding to lamda if (T-lamda I)^(p) (x) = 0 for some positive integer p. Is this enough to say that statement is false?
     
  2. jcsd
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