Show that for any n there is a $\displaystyle T:C^n \rightarrow C^n$ so that the invariant subspaces of T are $\displaystyle \{\vec{0}\} \subsetneq V_1 \subsetneq ... \subsetneq V_n = C^n$ and there aren't any others.

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- Apr 21st 2009, 10:40 AMvincisonfireT-Invariant spaces
Show that for any n there is a $\displaystyle T:C^n \rightarrow C^n$ so that the invariant subspaces of T are $\displaystyle \{\vec{0}\} \subsetneq V_1 \subsetneq ... \subsetneq V_n = C^n$ and there aren't any others.