grandes-ecoles 2017 Q11

grandes-ecoles · France · x-ens-maths__pc Matrices Matrix Norm, Convergence, and Inequality

Let $A \in M _ { n } ( \mathbb { C } )$. Show the formula $$\lim _ { k \rightarrow + \infty } \left\| A ^ { k } \right\| ^ { 1 / k } = \rho ( A )$$

Let $A \in M _ { n } ( \mathbb { C } )$. Show the formula
$$\lim _ { k \rightarrow + \infty } \left\| A ^ { k } \right\| ^ { 1 / k } = \rho ( A )$$