How do I find a linear transformation from P4 to P4 (polynomial space of at most degree 4) such that the linear transformation is nonzero, but the transformation to any positive power n is zero? Thanks!
2026-04-01 22:05:02.1775081102
Linear transformation from $P_4$ to $P_4$
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1
The transformation with matrix $\begin{pmatrix} 0&0&0&0&1\\0&0&0&0&0\\0&0&0&0&0\\0&0&0&0&0\\0&0&0&0&0\end{pmatrix}$.
Put differently, $T(a_1x^4+a_2x^3+a_3x^2+a_4x+a_5)=a_5x^4$.