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Homework Help: Linear Polynomial Transformation

  1. Feb 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Let [itex] T:P_m(\mathbb{F}) \mapsto P_{m+2}(\mathbb{F}) [/itex] such that [itex] Tp(z)=z^2 p(z) [/itex]. Would a suitable basis for range [itex] T [/itex] be [itex] (z^2, \dots, z^{m+2}) [/itex]?
  2. jcsd
  3. Feb 4, 2013 #2


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