grandes-ecoles 2013 QIII.E.3

grandes-ecoles · France · centrale-maths2__pc Invariant lines and eigenvalues and vectors Geometric interpretation of eigenstructure
Show that for every endomorphism $f$ of $\mathbb{R}^2$, there exist non-negative reals $k$ and $\ell$, a plane rotation $\rho_t$ and a reflection $\sigma_{t'}$ such that $f = k\rho_t + \ell\sigma_{t'}$.
Show that for every endomorphism $f$ of $\mathbb{R}^2$, there exist non-negative reals $k$ and $\ell$, a plane rotation $\rho_t$ and a reflection $\sigma_{t'}$ such that $f = k\rho_t + \ell\sigma_{t'}$.