Linear Polynomial Transformation

[Shoelace Thm.]

Homework Statement

Let T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F}) such that Tp(z)=z^2 p(z). Would a suitable basis for range T be (z^2, \dots, z^{m+2})?

 

[Dick]

Homework Statement

Let T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F}) such that Tp(z)=z^2 p(z). Would a suitable basis for range T be (z^2, \dots, z^{m+2})?

I don't see any problem with that. It spans T(P_m), yes?