Exercise 2.4.18

Answers

With the same notation we have that

L_{A} ϕ_{β} (p (x)) = (\begin{matrix} 0 & 1 & 0 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 3 \end{matrix}) (\begin{matrix} 1 \\ 1 \\ 2 \\ 1 \end{matrix}) = (\begin{matrix} 1 \\ 4 \\ 3 \end{matrix})

and

ϕ_{γ} T (p (x)) = ϕ_{γ} (1 + 4 x + 3 x^{2}) = (\begin{matrix} 1 \\ 4 \\ 3 \end{matrix}) .

So they are the same.

jephianlin

2011-06-27 00:00