grandes-ecoles 2014 QIE

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 $(A, B) \mapsto \operatorname{Tr}({}^t A \times B)$.
For $n \in \mathbb{N}^*$ and $A \in \mathcal{M}_d(\mathbb{R})$, compare $\left\|A^n\right\|$ and $\|A\|^n$.

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

For $n \in \mathbb{N}^*$ and $A \in \mathcal{M}_d(\mathbb{R})$, compare $\left\|A^n\right\|$ and $\|A\|^n$.

Paper Questions

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