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Find T cyclic operator that has exactly N distinct T-invariant subspaces

crypt50

New member
Jun 29, 2013
21
Let T be a cyclic operator on $R^3$, and let N be the number of distinct T-invariant subspaces. Prove that either N = 4 or N = 6 or N = 8. For each possible value of N, give (with proof) an example of a cyclic operator T which has exactly N distinct T-invariant subspaces.

Am I supposed to assume that T is a linear operator on V, after assuming that V is a finite dimensional vector space? Also, I think I'm supposed to use the dimension of subspaces, but I don't understand how it's supposed to be used.