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Cyclic Vector

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Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, Tv } is a base for V).

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Suppose that T is a linear operator on a two dimensional vector space V, and that T is not multiple of the identity transformation. Show that T has a cyclic vector (i.e., there exists v V such that {v, ...

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