Sea la aplicación lineal \(f:\mathbb{R}_3[X]\to\mathbb{R}_3[X]\), dada por \(\forall p(X)\in\mathbb{R}_3[X]\), es \(f(p(X))=p(x)-2\frac{d}{dX}p(X)\). ¿Cuánto es la traza de la matriz asociada a la aplicación \(f\)?
(%i1) f ( p ) : = p − 2 · diff ( p , x ) ;

\[\operatorname{ }\operatorname{f}(p)\operatorname{:=}p-2 \left( \frac{d}{d x} p\right) \]

(%i2) f ( [ 1 , x , x ^ 2 , x ^ 3 ] ) ;

\[\operatorname{ }\left[ 1\operatorname{,}x-2\operatorname{,}{{x}^{2}}-4 x\operatorname{,}{{x}^{3}}-6 {{x}^{2}}\right] \]

(%i4) A : matrix ( [ 1 , 0 , 0 , 0 ] , [ − 2 , 1 , 0 , 0 ] , [ 0 , − 4 , 1 , 0 ] , [ 0 , 0 , − 6 , 1 ] ) $
A : transpose ( A ) ;

\[\operatorname{ }\begin{bmatrix}1 & -2 & 0 & 0\\ 0 & 1 & -4 & 0\\ 0 & 0 & 1 & -6\\ 0 & 0 & 0 & 1\end{bmatrix}\]

(%i5) mat_trace ( A ) ;

\[\operatorname{ }4\]

Created with wxMaxima.