Question: Let Pj(R) be the vector space over the reals of degree j polynomials. Show that if j k then Pj(R) is an invariant subspace

Let Pj(R) be the vector space over the reals of degree j polynomials. Show that if j ≤ k then Pj(R) is an invariant subspace of Pk(R) under the differentiation operator. In P7(R), does any of P0(R), . . . , P6(R) have an invariant complement?

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