grandes-ecoles 2014 QID

grandes-ecoles · France · centrale-maths1__mp Matrices Matrix Norm, Convergence, and Inequality

In the rest of the problem, we denote by $\|\cdot\|$ the norm associated with the inner product $(A, B) \mapsto \operatorname{Tr}({}^t A \times B)$.
Show that: $\forall (A, B) \in \mathcal{M}_d(\mathbb{R})^2, \|A \times B\| \leqslant \|A\| \cdot \|B\|$.

In the rest of the problem, we denote by $\|\cdot\|$ the norm associated with the inner product $(A, B) \mapsto \operatorname{Tr}({}^t A \times B)$.

Show that: $\forall (A, B) \in \mathcal{M}_d(\mathbb{R})^2, \|A \times B\| \leqslant \|A\| \cdot \|B\|$.

Paper Questions

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