grandes-ecoles 2024 Q6

grandes-ecoles · France · x-ens-maths__psi Sequences and Series Matrix Exponentials and Series of Matrices
Let $v = (v_k)_{k \geqslant 0}$ be another sequence of complex numbers. Show that $$\mathbb{M}_n(u) \cap \mathbb{M}_n(v) \subset \mathbb{M}_n(u+v) \cap \mathbb{M}_n(u \star v)$$
Let $v = (v_k)_{k \geqslant 0}$ be another sequence of complex numbers. Show that
$$\mathbb{M}_n(u) \cap \mathbb{M}_n(v) \subset \mathbb{M}_n(u+v) \cap \mathbb{M}_n(u \star v)$$