grandes-ecoles 2024 Q2

grandes-ecoles · France · x-ens-maths__pc Matrices Matrix Norm, Convergence, and Inequality
Verify that $(A, B) \mapsto \langle A, B \rangle$ is an inner product on the vector space $\mathscr{M}_{d}(\mathbb{R})$. We denote by $\|A\| = \sqrt{\langle A, A \rangle}$ the associated norm.
Verify that $(A, B) \mapsto \langle A, B \rangle$ is an inner product on the vector space $\mathscr{M}_{d}(\mathbb{R})$. We denote by $\|A\| = \sqrt{\langle A, A \rangle}$ the associated norm.