\( \textbf{Produits scalaires} \\ \begin{array}{rl} \text{Lagrange} & \langle P,Q \rangle = P(\alpha_0)Q(\alpha_0) + P(\alpha_1)Q(\alpha_1) + \dots + P(\alpha_n)Q(\alpha_n) \\ \text{Géométrique} & \vec u \cdot \vec v = |\!|\vec u|\!| |\!|\vec v|\!| \cos(\vec u, \vec v) \\ \mathbb R^n & \langle (x_1, \dots, x_n),(y_1, \dots, y_n) \rangle = x_1y_1 + \dots + x_ny_n \\ \mathscr M_{n,1} & \langle X,Y \rangle = X^TY \\ \mathscr M_{n,m} & \langle A,B \rangle = \text{Tr }(A^TB) \\ \mathscr C^0([a;b],\mathbb R) & \langle f,g \rangle = \int_a^b fg \\ \mathbb R[X] & \langle P,Q \rangle = \langle \sum a_jXj,\sum b_jX_j \rangle = \sum a_jb_j \end{array} \)