grandes-ecoles 2017 Q3

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

Let $A \in M _ { n } ( \mathbb { C } )$. We denote by $a _ { i , j }$ the coefficient of $A$ with row index $i$ and column index $j$. Show that $$\| A \| = \max _ { 1 \leqslant j \leqslant n } \left( \sum _ { i = 1 } ^ { n } \left| a _ { i , j } \right| \right)$$

Let $A \in M _ { n } ( \mathbb { C } )$. We denote by $a _ { i , j }$ the coefficient of $A$ with row index $i$ and column index $j$. Show that
$$\| A \| = \max _ { 1 \leqslant j \leqslant n } \left( \sum _ { i = 1 } ^ { n } \left| a _ { i , j } \right| \right)$$

Paper Questions

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