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tinynerdi
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Homework Statement
It is possible for a generalized eigenvector of a linear operator T to correspond to a scalar that is not an eigenvalue of T.
Homework Equations
There is a definition of generalized eigenvector of T corresponding to lamda.
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?