Reconnaître les endomorphismes de \(\R^3\) définis par les expressions analytiques dans la base canonique :
\(\begin{cases} 3x' = 2x+2y+z \cr 3y' = -2x+y+2z \cr 3z' = x-2y+2z \cr\end{cases}\)
\(\begin{cases} 9x' = 8x+y-4z \cr 9y' = -4x+4y-7z \cr 9z'=x+8y+4z \cr\end{cases}\)
\(\begin{cases} 3x' = -2x+2y-z \cr 3y' = 2x+y-2z \cr 3z' = -x-2y-2z \cr\end{cases}\)
\(\begin{cases} 4x' = -2x - y\sqrt6 + z\sqrt6 \cr 4y' = x\sqrt6 + y + 3z \cr 4z' = -x\sqrt6 + 3y + z \cr \end{cases}\)
\(\begin{cases}x' = \frac x{\sqrt3} + \frac y{\sqrt2} - \frac z{\sqrt6} \cr y' = \frac x{\sqrt3} + \frac {2z}{\sqrt6} \cr z' = \frac x{\sqrt3} - \frac y{\sqrt2} - \frac z{\sqrt6} \cr\end{cases}\)
\(\begin{cases} 3x' = x+2y+2z \cr 3y' = 2x+y-2z \cr 3z' = 2x-2y+z \cr\end{cases}\)
\(\begin{cases} 7x' = -2x+6y-3z \cr 7y' = 6x+3y+2z \cr 7z' = -3x+2y+6z \cr\end{cases}\)
\(\begin{cases} 3x' = 2x-2y+z \cr 3y' = -2x-y+2z \cr 3z' = x+2y+2z \cr\end{cases}\)
\(\begin{cases} 3x' = 2x+y+2z \cr 3y' = 2x-2y-z \cr 3z' = -x-2y+2z \cr\end{cases}\)
\(\begin{cases} 4x' = -x+3y-z\sqrt6 \cr 4y' = 3x-y-z\sqrt6 \cr 4z' = x\sqrt6+y\sqrt6+2z \cr\end{cases}\)
\(\begin{cases} 15x'=5x-10z \cr 15y' = -8x+5y+6z \cr 15z' = 6x-10y+8z \cr\end{cases}\) [rotproj]