Linear Polynomial Transformation

1. Feb 4, 2013

Shoelace Thm.

1. The problem statement, all variables and given/known data
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 $(z^2, \dots, z^{m+2})$?

2. Feb 4, 2013

Dick

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