# Linear operators

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Let T be a linear operator on a finite dimensional vector space V. Suppose the minimal polynomial for T is of the form P^n where p is an irreducible polynomial over the scalar field. Show that there is a vector x in V such that the T-annihilator of x is p^n.

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Please see the attachment.

is a linear operator of a finite dimensional vector space . Assume . The minimal polynomial for is , where is an irreducible polynomial over the scalar field. This means .

For each , we can define the -annihilator as . In your ...

#### Solution Summary

This is a proof regarding linear operators, vectors, and t-annihilators. Irreducible polynomials over the scalar fields are analyzed.

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