grandes-ecoles 2022 Q5

grandes-ecoles · France · centrale-maths1__pc Not Maths

Show that the application $\phi : (P, Q) \mapsto \phi(P, Q) = \int_0^1 P(t)Q(t)\,\mathrm{d}t$ defines an inner product on $\mathbb{R}_{n-1}[X]$.

Show that the application $\phi : (P, Q) \mapsto \phi(P, Q) = \int_0^1 P(t)Q(t)\,\mathrm{d}t$ defines an inner product on $\mathbb{R}_{n-1}[X]$.