Question

Asked Dec 31, 2019

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Let D be the differentiation operator on P(R), the space of polynomials over R. Prove that there exists no polynomial g(t) for which g(D) = T0. Hence D has no minimal polynomial.

Step 1

Let *D* be the differentiation operator on *P*(*R*), the space of polynomials over *R*.

To prove- There exists no polynomial *g*(*t*) for which *g*(*D*) =* T*_{0}.

Hence *D* has no minimal polynomial.

Step 2

Let us suppose in contradiction that a polynomial ( *g*(*t *) ) of degree *n*.

Such that

Step 3

After differentiating it n times, the result is a non zero con...

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