grandes-ecoles 2014 QIA

grandes-ecoles · France · centrale-maths1__mp Matrices Matrix Norm, Convergence, and Inequality
Show that, for every polynomial $P \in \mathbb{C}[X]$, the map $f_P : A \mapsto P(A)$ is a continuous function from $\mathcal{M}_d(\mathbb{R})$ to $\mathcal{M}_d(\mathbb{C})$. 
Show that, for every polynomial $P \in \mathbb{C}[X]$, the map $f_P : A \mapsto P(A)$ is a continuous function from $\mathcal{M}_d(\mathbb{R})$ to $\mathcal{M}_d(\mathbb{C})$.
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