grandes-ecoles 2017 QI.B.2

grandes-ecoles · France · centrale-maths2__psi Matrices Matrix Norm, Convergence, and Inequality
Verify the following property: $\forall A \in \mathcal { M } _ { n } ( \mathbb { C } ) , \forall Y \in \mathbb { C } ^ { n } \quad \| A Y \| _ { \infty } \leqslant n \| A \| _ { 0 } \cdot \| Y \| _ { \infty }$ 
Verify the following property: $\forall A \in \mathcal { M } _ { n } ( \mathbb { C } ) , \forall Y \in \mathbb { C } ^ { n } \quad \| A Y \| _ { \infty } \leqslant n \| A \| _ { 0 } \cdot \| Y \| _ { \infty }$
Paper Questions
QI.A.1 QI.A.2 QI.A.3 QI.A.4 QI.B.1 QI.B.2 QII.A.1 QII.A.2 QII.A.3 QII.A.4 QII.A.5 QII.B.1 QII.B.2 QII.B.3 QII.C QII.D.1 QII.D.2 QII.E.1 QII.E.2 QII.E.3 QIII.A QIII.B.1 QIII.B.2 QIII.C QIII.D.1 QIII.D.2 QIII.E.1 QIII.E.2 QIII.E.3 QIV.A.1 QIV.A.2 QIV.B.1 QIV.B.2 QIV.B.3 QIV.C.1 QIV.C.2 QIV.C.3 QIV.D.1 QIV.D.2 QV.A QV.B.1 QV.B.2 QV.B.3 QV.B.4