grandes-ecoles 2014 QIC

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 all integers $i, j$ between 1 and $d$ and every matrix $A \in \mathcal{M}_d(\mathbb{R})$, compare $\left|A_{i,j}\right|$ and $\|A\|$.

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 all integers $i, j$ between 1 and $d$ and every matrix $A \in \mathcal{M}_d(\mathbb{R})$, compare $\left|A_{i,j}\right|$ and $\|A\|$.

Paper Questions

QIA QIB QIC QID QIE QIIA QIIB QIIC QIIIA1 QIIIA2 QIIIA3 QIIIB1 QIIIB2 QIIIB3 QIIIB4 QIVA QIVB QIVC QVA QVB QVC QVD QVE QVF QVG QVH QVI QVJ