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?