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Let T be an operator on a finite-dimensional complex vector space V, and suppose that dim...

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Advance Math

Let T be an operator on a finite-dimensional complex vectorspace V, and suppose that dim Null T = 3, dimNullT2 =6. Prove thatT does not have a square root; i.e. there does not exist any S ∈ L(V) such that S2 = T.

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